From 88de7574f2e3837d4aeb0f3d63f0017c499f5eac Mon Sep 17 00:00:00 2001 From: Rohan Arun Date: Sat, 17 Oct 2026 12:09:52 -0400 Subject: [PATCH 1/4] Conditional kappa = 0.001733427039589844234749 (bit-bound): idle-remainder donors on PR3148's T740 fill Idle remainders of partially used bins donate axes, under PR1252's commuting rule, to unhosted idle children of the same replica and port (cap 51), followed by PR3184's stars. 391,964 axis moves; complex root 0.00173477055711151316 exceeds the PR589 bit saving, so kappa is bit-capped: +3.238e-6 over PR3184. Independent verifier with eight rejected controls; native admission and outer release with the overlay not rerun. Done with help from OpenCode (Space bunny free). Co-Authored-By: Claude Opus 5.5 Claude-Session: https://claude.ai/code/session_011S35E2acyQDaVRjPRw4TDy --- .../AUDIT.json | 18 + .../BINS.json.gz | Bin 0 -> 239829 bytes .../CLAIM.json | 30 + .../MOVES.json.gz | Bin 0 -> 1163384 bytes .../PR3148-PROVIDERS.json | 842 ++++++++++++++++++ .../README.md | 118 +++ .../RESULT.json | 55 ++ .../VERIFY.json | 11 + .../rank7-idle-remainder-donors-t740/build.py | 209 +++++ .../verify.py | 175 ++++ 10 files changed, 1458 insertions(+) create mode 100644 research/rank7-idle-remainder-donors-t740/AUDIT.json create mode 100644 research/rank7-idle-remainder-donors-t740/BINS.json.gz create mode 100644 research/rank7-idle-remainder-donors-t740/CLAIM.json create mode 100644 research/rank7-idle-remainder-donors-t740/MOVES.json.gz create mode 100644 research/rank7-idle-remainder-donors-t740/PR3148-PROVIDERS.json create mode 100644 research/rank7-idle-remainder-donors-t740/README.md create mode 100644 research/rank7-idle-remainder-donors-t740/RESULT.json create mode 100644 research/rank7-idle-remainder-donors-t740/VERIFY.json create mode 100644 research/rank7-idle-remainder-donors-t740/build.py create mode 100644 research/rank7-idle-remainder-donors-t740/verify.py diff --git a/research/rank7-idle-remainder-donors-t740/AUDIT.json b/research/rank7-idle-remainder-donors-t740/AUDIT.json new file mode 100644 index 0000000000..775b31ed35 --- /dev/null +++ b/research/rank7-idle-remainder-donors-t740/AUDIT.json @@ -0,0 +1,18 @@ +{ + "binding": "bit", + "complex_root_lower": "17347705571115131604951/10000000000000000000000000", + "fill_rebound": true, + "kappa": "17334270395898442347489999999999999999999998999999999999999999999999/10000000000000000000000000000000000000000000000000000000000000000000000", + "moves": 391964, + "rejected_controls": { + "axis_moved_twice": "axis not in donor remainder", + "dropped_move": "declared profile", + "foreign_axis": "axis not in donor remainder", + "hosted_axis_from_used_prefix": "axis not in donor remainder", + "hosted_receiver": "receiver must be unhosted", + "kappa_above_bit": "headline kappa", + "next_root_grid": "complex root bracket", + "receiver_donates": "receiver must be unhosted" + }, + "status": "PASS_IDLE_REMAINDER_DONOR_AUDIT" +} diff --git a/research/rank7-idle-remainder-donors-t740/BINS.json.gz b/research/rank7-idle-remainder-donors-t740/BINS.json.gz new file mode 100644 index 0000000000000000000000000000000000000000..fc2446437c8ba8b5f10aa4cefd5290927c64dc26 GIT binary patch literal 239829 zcmd431z1$w->8jJgLFtYQc6ln3J6Gts0auWQqm&Q2n-=1Qi60yS%83~zznT4DBUeJ zbPwO2q4aq;|MR}*JLi0#*S_u*dj@b_d#$ziTK8|$1%pr!|1KVW{MO=NBI=Z}!*yf2 z`ohA9>#L*;i}uW`^IUw-lrk+te@}^$~}Ib-3xZ zzgU$at`FbLJ%rmHZXE7c9nRYxE-riRwH>a|9d1e@>IQy{z$Zoy*ADl9+#$T!>!9jz zrs`me?l9nR*WhrX>TuBjK4k#>6t9Dss>2?yiZ_P`E34ZYM%-oxKYol%EJ|*yZm&r8 z0GYi-$(cpTs;e*Vl5bxDZz`6?%PQ2IM(qw3PVL;tncy4nud zx;9cytFik+jjFVLO-!OLiZ)WTtSU~OCJ4M5^bu2yTX@%WiXWgI^*UL@5w>`z4b7Pwd`$y4Ya!00kt^OKKN9)E4?o3;oRGxQF)e9vX5trF_9SZl|L}rz| 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"gain_over_pr3184": "1618989177996737327/500000000000000000000000", + "gain_over_pr3148": "3649544911247222863/1000000000000000000000000", + "profile": { + "1": 16353294, + "2": 4837720, + "3": 1533431, + "4": 679320, + "5": 147055, + "8": 53280, + "42": 32303, + "45": 34720, + "48": 48434, + "49": 47026, + "50": 15320, + "51": 104766 + }, + "T": 740, + "changed_hypothesis": "idle remainders of partially hosted bins donate axes (PR1252 rule) to unhosted idle children; receivers capped at 51", + "status": "author-checked conditional candidate; native admission, overlay-aware controller audit and bit-binding outer release not rerun", + "credits": "PR1252 Gonzalo-Mier; star class Gueorgui Maissouradze; PR3148 Jeremy Diviney; PR3133/PR3042 dcharb78; PR2979 Marius-Paul Dumitrean; OpenCode (Space bunny free); Anthropic Claude" +} \ No newline at end of file diff --git a/research/rank7-idle-remainder-donors-t740/MOVES.json.gz b/research/rank7-idle-remainder-donors-t740/MOVES.json.gz new file 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b/research/rank7-idle-remainder-donors-t740/README.md new file mode 100644 index 0000000000..ec5fd9796d --- /dev/null +++ b/research/rank7-idle-remainder-donors-t740/README.md @@ -0,0 +1,118 @@ +# Idle-remainder donors on PR3148's T740 fill: the complex side passes the bit side; conditional κ = 0.001733427039589844234749 − 10⁻⁴⁶ − 10⁻⁷⁰ + +**Author-checked conditional candidate; not maintainer-reviewed.** The selected record on +`main` is still #1094. This package stacks on the open PR3148 (Jeremy Diviney) and extends +the idle-axis exchanges of PR3184. PR3133's words, the helper widths, and PR3148's fill rows, +order and dispatch are all unchanged. + +| | complex root lower (10⁻²⁵) | binding | κ headline | +|---|---|---|---| +| PR3148 | 0.0017297774946785970118869 | complex | 0.001729777494678597011886 − … | +| PR3184 (stars on fully idle 48s) | 0.0017301890612338507600957 | complex | 0.001730189061233850760095 − … | +| **this** | **0.0017347705571115131604951** | **bit (#589)** | **0.001733427039589844234749 − 10⁻⁴⁶ − 10⁻⁷⁰** | + +The gain is **+3.238e-6 (+0.187%) over PR3184** and +3.650e-6 over PR3148. The complex +supplier now exceeds the bit supplier's 0.001733427039589844234749, the constant pinned in the +T74 outer ledger. **The bit side binds, so κ is capped there.** + +## Changed hypothesis + +PR3184 moved axes only among *completely* idle capacity-48 children. But every bin that +helpers use only partially leaves an idle **remainder child**, whose axes are the recipe axes +`[used, cap)`. That holds for every hosted #1094 child: the hosted `IDLE-REMAINDER-FRAMES` equal +`orthogonal_axes[hosted:]`. PR3148's idle bill is `{1: 173160, 3: 48951, 5: 13875, 48: 282569}`. + +Removing a small child is far more valuable than reshaping 48s. Moving one axis from a rank-1 +remainder into a 48 removes `1·ln 73` of moment weight, against `0.18` for a whole +`48+48 → 45+51` pair. + +Here any remainder, hosted or not, may **donate** axes to a **fully idle (unhosted) receiver** +in the same replica and port. Each moved axis follows PR1252's rule: + +- it commutes with all of the receiver's axes at the time it moves; +- it commutes with every stage entry/exit X and Y translation and the terminal Y translation; +- it commutes with both children's terminal translations. + +Receivers stay at or below rank 51, so `73² = 5329 > 2·51² = 5202`. Moved axes come from the +donor's idle remainder, so they are orthogonal to its hosted prefix axes; the recipe sets are +orthonormal. Each group's axis multiset is unchanged. + +The construction runs in two phases: + +1. **Drain remainders.** Remainders are drained smallest first, one axis at a time, into the + largest legal receiver. +2. **Stars.** PR3184's exact star optimum runs on the untouched fully idle 48s. + +This produces 391,964 axis moves, from 138,369 donor children into 167,112 receivers. The idle +bill becomes: + +`{1:149514, 2:15880, 3:14951, 5:13855, 42:32303, 45:34720, 48:48434, 49:47026, 50:15320, 51:104766}` + +The rank mass is unchanged at `65088·740`. + +## Reproduce + +```sh +# PR3148's deterministic materializer (head f2927a4b) -> /tmp/t740 +python3 -B research/rank7-idle-remainder-donors-t740/build.py --t740 /tmp/t740 # ~20 s +python3 -B research/rank7-idle-remainder-donors-t740/verify.py --t740 /tmp/t740 # ~1 min +``` + +**Pinned inputs:** + +- DATA-PHASES (`c5916ff3…`) +- the decoded fill payload (`8f4d6965…`) +- ORDER (`927226d7…`) and DISPATCH (`90edc935…`) +- PR3148's provider widths (`PR3148-PROVIDERS.json`, `52eb0d85…`) + +The build reproduces PR3148's idle bill exactly. + +**`verify.py` does not import `build.py`.** It re-derives: + +- that donor axes lie in the donor's own remainder; +- that receivers are unhosted, and no child both donates and receives; +- the unit and orthogonal-at-receipt checks, and the commuting rule; +- the rank cap; +- the profile and rank mass; +- the complex root bracket, using its own interval arithmetic at 10⁻⁷²; +- `κ = min(floor₂₄(complex_lower), bit) − 10⁻⁴⁶ − 10⁻⁷⁰`, with gates against PR3148 and PR3184. + +It also rebinds BINS to the fill. Eight mutation controls are rejected: + +- a hosted receiver; +- an axis taken from the hosted prefix; +- a foreign axis; +- an axis moved twice; +- a receiver that also donates; +- a dropped move; +- the next root grid point; +- κ above the bit cap. + +## Scope and remaining obligations + +- **New hypothesis beyond PR1252/PR3184:** hosted remainders may donate. The moved axes are + orthogonal to the hosted prefix and obey the full commuting rule, but no hosted-controller + argument is given here. PR1252's admitted audit covered only unhosted pairs. +- **Not rerun:** PR3148/PR3133's native admission, the controller/owner audit (`audit_mixed.py` + must read the axis overlay) and the outer release. The outer ledger asserts + `complex < bit`, so a bit-binding release needs its ledger branch, and the halving pin + `[5329,4608]` must become `[5329,5202]`. +- Because the bit side now binds, further complex-side packing gains do not raise κ until the + bit supplier improves. All inherited all-size/compiler, realization, precision/tape, recovery + and analytic obligations remain. PR3148 itself is unreviewed. + +## Credit + +- Gonzalo-Mier (PR1252): the move, the rule and the pricing. +- Guéorgui Maissouradze: the star class. +- Jeremy Diviney (PR3148): the fill. +- dcharb78 (PR3133, PR3042). +- Marius-Paul Dumitrean (PR2979). +- Jeremy Kothe (PR3015). +- Nick Petalas (PR3024). +- DreamingOfClouds and eumemic: the #589/#555 bit supplier. +- The data-phase and T37-envelope lineage. + +Prepared by Rohan Arun. Done with help from **OpenCode (Space bunny free)**, whose +partially-used-bin centre idea this package generalizes, and with Anthropic Claude assistance. +Apache-2.0. diff --git a/research/rank7-idle-remainder-donors-t740/RESULT.json b/research/rank7-idle-remainder-donors-t740/RESULT.json new file mode 100644 index 0000000000..2bbb2926bb --- /dev/null +++ b/research/rank7-idle-remainder-donors-t740/RESULT.json @@ -0,0 +1,55 @@ +{ + "status": "PASS_IDLE_REMAINDER_DONOR_EXCHANGES_T740", + "T": 740, + "axis_moves": 391964, + "donor_children": 138369, + "receiver_children": 167112, + "idle_before": { + "1": 173160, + "3": 48951, + "5": 13875, + "48": 282569 + }, + "idle_after": { + "1": 149514, + "2": 15880, + "3": 14951, + "5": 13855, + "42": 32303, + "45": 34720, + "48": 48434, + "49": 47026, + "50": 15320, + "51": 104766 + }, + "profile": { + "1": 16353294, + "2": 4837720, + "3": 1533431, + "4": 679320, + "5": 147055, + "8": 53280, + "42": 32303, + "45": 34720, + "48": 48434, + "49": 47026, + "50": 15320, + "51": 104766 + }, + "complex_root": [ + "17347705571115131604951/10000000000000000000000000", + "2168463196389391450619/1250000000000000000000000" + ], + "complex_root_decimal": "17347705571115131604951e-25", + "bit": "1733427039589844234749/1000000000000000000000000", + "binding": "bit", + "kappa": "17334270395898442347489999999999999999999998999999999999999999999999/10000000000000000000000000000000000000000000000000000000000000000000000", + "kappa_decimal": "0.0017334270395898442347489999999999999999999998999999999999999999999999", + "gain_over_pr3184": "1618989177996737327/500000000000000000000000", + "gain_over_pr3148": "3649544911247222863/1000000000000000000000000", + "max_child_rank": 51, + "halving": [ + 5329, + 5202 + ] +} diff --git a/research/rank7-idle-remainder-donors-t740/VERIFY.json b/research/rank7-idle-remainder-donors-t740/VERIFY.json new file mode 100644 index 0000000000..ac9bd95d36 --- /dev/null +++ b/research/rank7-idle-remainder-donors-t740/VERIFY.json @@ -0,0 +1,11 @@ +{ + "commands": [ + [ + "python3", + "-B", + "research/rank7-idle-remainder-donors-t740/verify.py" + ] + ], + "expected": "PASS_IDLE_REMAINDER_DONOR_AUDIT", + "seconds": 70 +} \ No newline at end of file diff --git a/research/rank7-idle-remainder-donors-t740/build.py b/research/rank7-idle-remainder-donors-t740/build.py new file mode 100644 index 0000000000..87ccf74f2b --- /dev/null +++ b/research/rank7-idle-remainder-donors-t740/build.py @@ -0,0 +1,209 @@ +#!/usr/bin/env python3 +# SPDX-License-Identifier: Apache-2.0 +"""Idle-remainder donor exchanges on PR3148's T740 fill of PR3133's words. + +Every idle remainder of a (replica, port) - including the remainder of a partially hosted bin, +whose axes are the recipe axes [used, cap) - may donate axes to a fully idle (unhosted) child of +the same replica and port. Each moved axis obeys PR1252's commuting rule (commutes with all of the +receiver's current axes, every stage entry/exit X and Y translation, the terminal Y translation and +both children's terminal translations). Receivers are capped at rank 51 (73^2 > 2*51^2). +Phase 1 drains remainders smallest-first into the largest legal receiver; phase 2 runs the +frontier1094 star optimum (PR3184) on the untouched fully idle rank-48 children. + +Inputs (pinned): DATA-PHASES.json on main; PR3148's materialized COMPOSED-FILL/ORDER/DISPATCH and +its PR3133 provider widths (PR3148-PROVIDERS.json, copied from PR3148 vendor/). +""" +import argparse, gzip, hashlib, itertools, json, math +from collections import Counter, defaultdict +from fractions import Fraction as Q +from pathlib import Path + +HERE = Path(__file__).resolve().parent +PHASES = HERE.parents[1] / 'research/adaptive-kernel-demotion/inputs/DATA-PHASES.json' +PIN = dict(phases='c5916ff312678f12aba403847643fbbc29f643acec60bdf836fa56cd3e8251fa', + fill_payload='8f4d6965ba573ff2b71fd7bf6b552643e086739d90bd73c55889502077638e00', + order='927226d702bf3cada076f4c459da9063c0df7e7154a62955cf75c40cf30215b9', + dispatch='90edc935320dd6264e98dc735d868df3c95f5901c70d7d96171001fcb295cce0', + providers='52eb0d85caa7b2d4a93acdf5011f52b793f61ddca86235fb03cd9a09397ad4cd') +T = 740 +LOCAL = {1: 2433, 2: 724, 3: 228, 4: 102, 5: 20, 8: 8} +IDLE_PR3148 = {1: 173160, 3: 48951, 5: 13875, 48: 282569} +BIT = Q('0.001733427039589844234749') # PR589 bit saving, as pinned in the T74 outer ledger +PR3148_KAPPA = Q('0.0017297774946785970118859999999999999999999998999999999999999999999999') +PR3184_KAPPA = Q('0.0017301890612338507600949999999999999999999998999999999999999999999999') + + +def need(ok, why): + if not ok: raise SystemExit('FAIL: ' + why) + + +def sha(b): return hashlib.sha256(b).hexdigest() +def dot(a, b): return (a & b).bit_count() & 1 +def Hf(r): return 0.0 if r == 0 else r * (73.0 / r) ** 0.00173 + + +def pgz(obj): + d = bytearray(gzip.compress(json.dumps(obj, sort_keys=True, separators=(',', ':')).encode(), mtime=0)); d[9] = 255 + return bytes(d) + + +# ---- exact root (rational intervals, directed rounding 1e-60) ---- +S = 10 ** 60 +def dn(x): return Q(math.floor(x * S), S) +def upr(x): return Q(math.ceil(x * S), S) +def atanh2(z, n): + s, p = Q(0), z + for j in range(n): s += p / (2 * j + 1); p *= z * z + return 2 * s, 2 * p / ((2 * n + 1) * (1 - z * z)) +L2 = atanh2(Q(1, 3), 120) +LN = {} +def lnr(r): + if r not in LN: + x, k = Q(73, r), 0 + while x > 2: x /= 2; k += 1 + a, e = atanh2((x - 1) / (x + 1), 80) + LN[r] = (dn(a + k * L2[0]), upr(a + e + k * (L2[0] + L2[1]))) + return LN[r] +def ex(x0, x1): + def ser(x): + s, t = Q(0), Q(1) + for n in range(1, 40): s += t; t = t * x / n + return s, t + a, _ = ser(x0); b, t = ser(x1) + return dn(a), upr(b + 2 * t) +def moment(prof, b): + W = 896 * T; lo = hi = Q(0) + for r, n in prof.items(): + l0, l1 = lnr(r); e0, e1 = ex(b * l0, b * l1); lo += n * r * e0; hi += n * r * e1 + return lo / (73 * W), hi / (73 * W) +def root(prof, digits=25): + f = lambda b: sum(n * r * (73 / r) ** b for r, n in prof.items()) / (73 * 896 * T) - 1 + a, c = 0.0, 0.01 + for _ in range(200): + m = (a + c) / 2 + if f(m) < 0: a = m + else: c = m + g = 10 ** digits; k0, k1 = int(a * g) - 10 ** 10, int(a * g) + 10 ** 10 + need(moment(prof, Q(k0, g))[1] < 1 and moment(prof, Q(k1, g))[0] > 1, 'bracket') + while k1 - k0 > 1: + k = (k0 + k1) // 2; lo, hi = moment(prof, Q(k, g)) + if hi < 1: k0 = k + elif lo > 1: k1 = k + else: raise SystemExit('wide interval') + return Q(k0, g), Q(k1, g) + + +def main(): + ap = argparse.ArgumentParser(description=__doc__) + ap.add_argument('--t740', type=Path, required=True, help='directory written by PR3148 materialize.py') + a = ap.parse_args() + raw = PHASES.read_bytes(); need(sha(raw) == PIN['phases'], 'phases pin') + rec = {r['port']: r for r in json.loads(raw)['recipes']} + fraw = gzip.decompress((a.t740 / 'COMPOSED-FILL.json.gz').read_bytes()); need(sha(fraw) == PIN['fill_payload'], 'fill pin') + need(sha((a.t740 / 'ORDER.json').read_bytes()) == PIN['order'] and sha((a.t740 / 'DISPATCH.json').read_bytes()) == PIN['dispatch'], 'order/dispatch pins') + praw = (HERE / 'PR3148-PROVIDERS.json').read_bytes(); need(sha(praw) == PIN['providers'], 'providers pin') + prov = json.loads(praw); order = json.loads((a.t740 / 'ORDER.json').read_bytes()) + disp = {(s, r): p for s, r, p in json.loads((a.t740 / 'DISPATCH.json').read_bytes())} + fill = json.loads(fraw) + need(fill['columns'] == ['time', 'helper', 'owner_replica', 'child', 'port', 'offset'] and fill['dispatch_overrides'] == [], 'fill format') + caps = {(p, c): ch['rank'] for p, r in rec.items() for c, ch in enumerate(r['idle_children'])} + AX = {(p, c): [int(v) for v in ch['orthogonal_axes']] for p, r in rec.items() for c, ch in enumerate(r['idle_children'])} + TR = {(p, c): int(ch['translation_after']) for p, r in rec.items() for c, ch in enumerate(r['idle_children'])} + PT = {p: [int(s[k]) for s in rc['stage_alignment'] for k in ('entry_Y', 'exit_Y', 'entry_X', 'exit_X')] + [int(rc['terminal_Y_translation'])] for p, rc in rec.items()} + used, top = Counter(), Counter() + for time, helper, rep, child, port, offset in fill['rows']: + s, r = order[time]; w = prov[disp[s, r]]['widths'][helper] + used[rep, child, port] += w; top[rep, child, port] = max(top[rep, child, port], offset + w) + need(all(used[k] == top[k] for k in used), 'compact helper prefixes') + groups = [] + for rep in range(T): + for p in range(112): + kids = [[c, used[rep, c, p]] for c in range(len(rec[p]['idle_children'])) if caps[p, c] - used[rep, c, p] > 0] + groups.append([rep, p, kids]) + idle = Counter(caps[p, c] - u for _, p, kids in groups for c, u in kids) + need(dict(idle) == IDLE_PR3148, 'idle bill equals PR3148') + + def legal(v, p, c, d, axes_d): + return all(dot(v, x) == 0 for x in axes_d) and all(dot(v, x) == 0 for x in PT[p]) and dot(v, TR[p, c]) == 0 and dot(v, TR[p, d]) == 0 + + def solve(p, kids): + rank = {c: caps[p, c] - u for c, u in kids}; axes = {c: AX[p, c][u:caps[p, c]] for c, u in kids} + hosted = {c: u > 0 for c, u in kids}; role = {c: None for c, _ in kids}; moves = [] + for c in sorted([c for c, u in kids if u > 0], key=lambda c: (rank[c], c)): + for v in list(axes[c]): + best = None + for d in sorted([d for d, _ in kids if not hosted[d] and role[d] != 'D' and d != c and rank[d] < 51], key=lambda d: (-rank[d], d)): + if rank[d] < rank[c] - 1: break + if legal(v, p, c, d, axes[d]): best = d; break + if best is None or Hf(rank[c] - 1) + Hf(rank[best] + 1) - Hf(rank[c]) - Hf(rank[best]) >= 0: continue + axes[c].remove(v); axes[best].append(v); rank[c] -= 1; rank[best] += 1 + role[c] = 'D'; role[best] = 'R'; moves.append([c, best, v]) + free = [c for c, u in kids if u == 0 and role[c] is None and caps[p, c] == 48] + if len(free) >= 2: + MV = {(d, r): [v for v in axes[d] if legal(v, p, d, r, axes[r])] for d in free for r in free if d != r} + best = [len(free) * Hf(48), []] + def match(c, leaves): + opts = [MV[c, l] for l in leaves] + if any(len(o) < 3 for o in opts): return None + def go(k, usedax): + if k == len(leaves): return [] + for trip in itertools.combinations([v for v in opts[k] if v not in usedax], 3): + rest = go(k + 1, usedax | set(trip)) + if rest is not None: return [(c, leaves[k], list(trip))] + rest + return None + return go(0, set()) + def assign(i, roles): + if i == len(free): + leaves = defaultdict(list) + for c in free: + if isinstance(roles[c], tuple): leaves[roles[c][1]].append(c) + cents = [c for c in free if roles[c] == 'c'] + if any(not leaves[c] for c in cents) or any(roles[x] != 'c' for x in leaves): return + mv = [] + for c in cents: + m = match(c, leaves[c]) + if m is None: return + mv += m + rk = [48 - 3 * len(leaves[c]) if roles[c] == 'c' else 51 if isinstance(roles[c], tuple) else 48 for c in free] + cost = sum(Hf(x) for x in rk) + if cost < best[0] - 1e-12: best[0], best[1] = cost, mv + return + c = free[i] + for opt in ['n', 'c'] + [('l', d) for d in free if d != c]: + roles[c] = opt; assign(i + 1, roles) + del roles[c] + assign(0, {}) + for c, l, trip in best[1]: + for v in trip: + axes[c].remove(v); axes[l].append(v); rank[c] -= 1; rank[l] += 1; moves.append([c, l, v]) + return moves, rank + + cache, moves, final = {}, [], Counter() + for rep, p, kids in groups: + key = (p, tuple(map(tuple, kids))) + if key not in cache: cache[key] = solve(p, kids) + mv, rank = cache[key] + moves += [[rep, p] + m for m in mv] + final.update(r for r in rank.values() if r) + prof = Counter({r: n * 9 * T for r, n in LOCAL.items()}); prof.update(final); prof = dict(sorted(prof.items())) + need(sum(r * n for r, n in prof.items()) == 65088 * T and 73 * 73 > 2 * max(prof) ** 2, 'mass and halving') + lo, hi = root(prof) + C = min(Q(math.floor(lo * 10 ** 24), 10 ** 24), BIT) + kappa = C - Q(1, 10 ** 46) - Q(1, 10 ** 70) + need(kappa > PR3184_KAPPA > PR3148_KAPPA, 'gates') + (HERE / 'BINS.json.gz').write_bytes(pgz(dict(T=T, columns=['replica', 'port', [['child', 'used']]], groups=[g for g in groups if g[2]]))) + (HERE / 'MOVES.json.gz').write_bytes(pgz(dict(columns=['replica', 'port', 'donor_child', 'receiver_child', 'axis'], moves=moves))) + donors = Counter(); + res = dict(status='PASS_IDLE_REMAINDER_DONOR_EXCHANGES_T740', T=T, axis_moves=len(moves), + donor_children=len({(m[0], m[1], m[2]) for m in moves}), receiver_children=len({(m[0], m[1], m[3]) for m in moves}), + idle_before={str(k): v for k, v in IDLE_PR3148.items()}, idle_after={str(k): v for k, v in sorted(final.items())}, + profile={str(k): v for k, v in prof.items()}, complex_root=[str(lo), str(hi)], + complex_root_decimal=f'{lo.numerator * 10**25 // lo.denominator}e-25', bit=str(BIT), binding='bit' if BIT < lo else 'complex', + kappa=str(kappa), kappa_decimal='0.0017334270395898442347489999999999999999999998999999999999999999999999', gain_over_pr3184=str(kappa - PR3184_KAPPA), gain_over_pr3148=str(kappa - PR3148_KAPPA), + max_child_rank=max(prof), halving=[5329, 2 * max(prof) ** 2]) + (HERE / 'RESULT.json').write_text(json.dumps(res, indent=1) + '\n') + print('PASS', float(lo), res['binding'], float(kappa), float(kappa - PR3184_KAPPA), len(moves)) + + +if __name__ == '__main__': + main() diff --git a/research/rank7-idle-remainder-donors-t740/verify.py b/research/rank7-idle-remainder-donors-t740/verify.py new file mode 100644 index 0000000000..39343120e2 --- /dev/null +++ b/research/rank7-idle-remainder-donors-t740/verify.py @@ -0,0 +1,175 @@ +#!/usr/bin/env python3 +# SPDX-License-Identifier: Apache-2.0 +"""Independent verifier (does not import build.py) for the idle-remainder donor exchanges. + +Re-derives from BINS / MOVES / DATA-PHASES: donor axes come from the donor's own idle remainder +(recipe axes [used, cap)); receivers are unhosted (used == 0); no child both donates and receives; +every moved axis is a unit vector orthogonal to all of the receiver's axes held at that moment and +commutes with every stage entry/exit X/Y translation, the terminal Y translation and both +children's terminal translations; final ranks <= 51; per-group axis multisets unchanged; the +complete profile and rank mass; an exact complex root bracket with its own interval arithmetic; +kappa = min(floor24(complex_lower), PR589 bit) - 1e-46 - 1e-70 and its gates. +Optional --t740 rebinds BINS to PR3148's materialized fill. Mutation controls must be rejected. +""" +import argparse, copy, gzip, hashlib, json +from collections import Counter, defaultdict +from fractions import Fraction as F +from pathlib import Path + +PKG = Path(__file__).resolve().parent +PHASES = PKG.parents[1] / 'research/adaptive-kernel-demotion/inputs/DATA-PHASES.json' +T = 740 +LOCAL = {1: 2433, 2: 724, 3: 228, 4: 102, 5: 20, 8: 8} +IDLE = {1: 173160, 3: 48951, 5: 13875, 48: 282569} +BIT = F('0.001733427039589844234749') +GATES = dict(PR3148=F('0.0017297774946785970118859999999999999999999998999999999999999999999999'), + PR3184=F('0.0017301890612338507600949999999999999999999998999999999999999999999999')) + + +class Reject(Exception): pass +def req(ok, why): + if not ok: raise Reject(why) +def load(p): + b = Path(p).read_bytes(); return json.loads(gzip.decompress(b) if b[:2] == b'\x1f\x8b' else b) +def par(a, b): return bin(a & b).count('1') & 1 + + +def audit(rec, bins, moves): + caps = {(p, c): ch['rank'] for p, r in rec.items() for c, ch in enumerate(r['idle_children'])} + G = {} + for rep, p, kids in bins['groups']: + req((rep, p) not in G and 0 <= rep < T and p in rec, 'group key') + G[rep, p] = {c: u for c, u in kids} + req(all(0 <= u < caps[p, c] for c, u in kids), 'used below capacity') + req(Counter(caps[p, c] - u for (rep, p), kids in G.items() for c, u in kids.items()) == Counter(IDLE), 'idle bill') + trans = {} + for p, rc in rec.items(): + trans[p] = {int(s[k]) for s in rc['stage_alignment'] for k in ('entry_X', 'exit_X', 'entry_Y', 'exit_Y')} | {int(rc['terminal_Y_translation'])} + for c, ch in enumerate(rc['idle_children']): + ax = [int(v) for v in ch['orthogonal_axes']] + req(all(par(v, v) == 1 for v in ax) and all(par(a, b) == 0 for i, a in enumerate(ax) for b in ax[i + 1:]), 'recipe axes orthonormal') + state = {} + def cur(rep, p, c): + k = (rep, p, c) + if k not in state: + u = G[rep, p][c]; state[k] = dict(axes=set(int(v) for v in rec[p]['idle_children'][c]['orthogonal_axes'][u:caps[p, c]]), role=None) + return state[k] + for m in moves: + rep, p, c, d, v = m + req((rep, p) in G and c in G[rep, p] and d in G[rep, p] and c != d, 'children of the group') + req(G[rep, p][d] == 0, 'receiver must be unhosted') + sc, sd = cur(rep, p, c), cur(rep, p, d) + req(sc['role'] != 'R' and sd['role'] != 'D', 'child both donates and receives') + own = set(int(x) for x in rec[p]['idle_children'][c]['orthogonal_axes'][G[rep, p][c]:caps[p, c]]) + req(v in sc['axes'] and v in own, 'axis not in donor remainder') + req(par(v, v) == 1 and all(par(v, x) == 0 for x in sd['axes']), 'axis not orthogonal to receiver axes') + tc = int(rec[p]['idle_children'][c]['translation_after']); td = int(rec[p]['idle_children'][d]['translation_after']) + req(all(par(v, x) == 0 for x in trans[p] | {tc, td}), 'axis does not commute with translations') + sc['axes'].discard(v); sd['axes'].add(v); sc['role'] = 'D'; sd['role'] = 'R' + req(len(sd['axes']) <= 51, 'rank above 51') + final = Counter() + for (rep, p), kids in G.items(): + for c, u in kids.items(): + r = len(state[rep, p, c]['axes']) if (rep, p, c) in state else caps[p, c] - u + if r: final[r] += 1 + return final + + +def mom(prof, b): + Q72 = 10 ** 72 + def rd(x): return F(x.numerator * Q72 // x.denominator, Q72) + def ru(x): return F(-((-x.numerator * Q72) // x.denominator), Q72) + def at(z, n): + s, p = F(0), z + for j in range(n): s += p / (2 * j + 1); p *= z * z + return 2 * s, 2 * p / ((2 * n + 1) * (1 - z * z)) + l2 = at(F(1, 3), 130); W = 896 * T; lo = hi = F(0) + for r, n in sorted(prof.items()): + y, k = F(73, r), 0 + while y >= 2: y /= 2; k += 1 + a, e = at((y - 1) / (y + 1), 90) + L0, L1 = rd(a + k * l2[0]), ru(a + e + k * (l2[0] + l2[1])) + def tay(x): + s, t = F(1), F(1) + for j in range(1, 34): t = t * x / j; s += t + return s, t * x / 34 * 3 + e0, _ = tay(b * L0); e1, t1 = tay(b * L1) + lo += n * r * rd(e0); hi += n * r * ru(e1 + t1) + return lo / (73 * W), hi / (73 * W) + + +def run(rec, bins, moves, result): + final = audit(rec, bins, moves) + prof = Counter({r: n * 9 * T for r, n in LOCAL.items()}); prof.update(final); prof = dict(sorted(prof.items())) + req({str(k): v for k, v in prof.items()} == result['profile'], 'declared profile') + req(sum(r * n for r, n in prof.items()) == 65088 * T, 'rank mass 65088*T') + req(max(prof) <= 51 and 73 * 73 > 2 * max(prof) ** 2, 'halving guard') + lo, hi = F(result['complex_root'][0]), F(result['complex_root'][1]) + req(hi - lo == F(1, 10 ** 25) and mom(prof, lo)[1] < 1 and mom(prof, hi)[0] > 1, 'complex root bracket') + C = min(F(lo.numerator * 10 ** 24 // lo.denominator, 10 ** 24), BIT) + kappa = C - F(1, 10 ** 46) - F(1, 10 ** 70) + req(kappa == F(result['kappa']), 'headline kappa') + for n, g in GATES.items(): req(kappa > g, 'kappa must exceed ' + n) + return prof, kappa, lo + + +def main(): + ap = argparse.ArgumentParser(description=__doc__) + ap.add_argument('--t740', type=Path) + ap.add_argument('--providers', type=Path, default=PKG / 'PR3148-PROVIDERS.json') + a = ap.parse_args() + if not __debug__: raise SystemExit('assertions required') + raw = PHASES.read_bytes() + req(hashlib.sha256(raw).hexdigest() == 'c5916ff312678f12aba403847643fbbc29f643acec60bdf836fa56cd3e8251fa', 'phases pin') + rec = {r['port']: r for r in json.loads(raw)['recipes']} + bins, mv, result = load(PKG / 'BINS.json.gz'), load(PKG / 'MOVES.json.gz')['moves'], load(PKG / 'RESULT.json') + rebound = False + if a.t740: + fraw = gzip.decompress((a.t740 / 'COMPOSED-FILL.json.gz').read_bytes()) + req(hashlib.sha256(fraw).hexdigest() == '8f4d6965ba573ff2b71fd7bf6b552643e086739d90bd73c55889502077638e00', 'fill pin') + prov = load(a.providers); order = load(a.t740 / 'ORDER.json'); disp = {(s, r): p for s, r, p in load(a.t740 / 'DISPATCH.json')} + used = Counter() + for time, helper, rep, child, port, offset in json.loads(fraw)['rows']: + s, r = order[time]; used[rep, child, port] += prov[disp[s, r]]['widths'][helper] + caps = {(p, c): ch['rank'] for p, r in rec.items() for c, ch in enumerate(r['idle_children'])} + derived = [[rep, p, [[c, used[rep, c, p]] for c in range(len(rec[p]['idle_children'])) if caps[p, c] - used[rep, c, p] > 0]] for rep in range(T) for p in range(112)] + req([g for g in derived if g[2]] == bins['groups'], 'BINS equal the fill') + rebound = True + prof, kappa, lo = run(rec, bins, mv, result) + rej = {} + first_hosted = next(i for i, m in enumerate(mv) if {c: u for c, u in next(g for g in bins['groups'] if g[0] == m[0] and g[1] == m[1])[2]}[m[2]] > 0) + rep, p, c, d, v = mv[first_hosted] + kids = {cc: u for cc, u in next(g for g in bins['groups'] if g[0] == rep and g[1] == p)[2]} + hosted_other = next((cc for cc, u in kids.items() if u > 0 and cc != c), None) + used_axis = int(rec[p]['idle_children'][c]['orthogonal_axes'][0]) + def mut(f): + x = copy.deepcopy(mv); f(x); return x + cases = dict( + hosted_receiver=mut(lambda x: x.__setitem__(first_hosted, [rep, p, c, hosted_other if hosted_other is not None else c, v])), + hosted_axis_from_used_prefix=mut(lambda x: x.__setitem__(first_hosted, [rep, p, c, d, used_axis])), + foreign_axis=mut(lambda x: x.__setitem__(first_hosted, [rep, p, c, d, 1 << 80])), + axis_moved_twice=mut(lambda x: x.insert(first_hosted + 1, list(x[first_hosted]))), + receiver_donates=mut(lambda x: x.append([rep, p, d, c, v])), + dropped_move=mut(lambda x: x.pop(first_hosted)), + ) + for name, x in cases.items(): + try: run(rec, bins, x, result) + except Reject as e: rej[name] = str(e) + else: raise SystemExit('mutation accepted: ' + name) + r2 = copy.deepcopy(result); r2['complex_root'] = [str(lo + F(1, 10 ** 25)), str(lo + F(2, 10 ** 25))] + try: run(rec, bins, mv, r2) + except Reject as e: rej['next_root_grid'] = str(e) + else: raise SystemExit('mutation accepted: next_root_grid') + r3 = copy.deepcopy(result); r3['kappa'] = str(F(result['kappa']) + F(1, 10 ** 24)) + try: run(rec, bins, mv, r3) + except Reject as e: rej['kappa_above_bit'] = str(e) + else: raise SystemExit('mutation accepted: kappa_above_bit') + out = dict(status='PASS_IDLE_REMAINDER_DONOR_AUDIT', moves=len(mv), fill_rebound=rebound, kappa=str(kappa), + complex_root_lower=str(lo), binding='bit' if BIT < lo else 'complex', rejected_controls=rej) + (PKG / 'AUDIT.json').write_text(json.dumps(out, indent=1, sort_keys=True) + '\n') + print('PASS_IDLE_REMAINDER_DONOR_AUDIT moves=%d controls=%d kappa=%s binding=%s' % (len(mv), len(rej), float(kappa), out['binding'])) + + +if __name__ == '__main__': + try: main() + except Reject as e: raise SystemExit('FAIL: ' + str(e)) From 5e4a3235169edddd033889da4e9f47635ff50c3e Mon Sep 17 00:00:00 2001 From: Rohan Arun Date: Sat, 17 Oct 2026 12:43:16 -0400 Subject: [PATCH 2/4] Register rank7-idle-remainder-donors-t740 for replay: TASK/SOURCES/VERIFY schema, open questions, read-only verifier Co-Authored-By: Claude Opus 5.5 Claude-Session: https://claude.ai/code/session_011S35E2acyQDaVRjPRw4TDy --- .../README.md | 10 +++ .../SOURCES.json | 30 +++++++ .../TASK.json | 78 +++++++++++++++++++ .../VERIFY.json | 27 ++++--- .../verify.py | 6 +- 5 files changed, 141 insertions(+), 10 deletions(-) create mode 100644 research/rank7-idle-remainder-donors-t740/SOURCES.json create mode 100644 research/rank7-idle-remainder-donors-t740/TASK.json diff --git a/research/rank7-idle-remainder-donors-t740/README.md b/research/rank7-idle-remainder-donors-t740/README.md index ec5fd9796d..7a26172c43 100644 --- a/research/rank7-idle-remainder-donors-t740/README.md +++ b/research/rank7-idle-remainder-donors-t740/README.md @@ -101,6 +101,16 @@ It also rebinds BINS to the fill. Eight mutation controls are rejected: bit supplier improves. All inherited all-size/compiler, realization, precision/tape, recovery and analytic obligations remain. PR3148 itself is unreviewed. +## Open next questions + +- **Is a hosted remainder a legal donor under the T74 controller contract?** PR1252's admitted + audit covered only unhosted children. First step: generalize the T74 `audit_mixed.py` + owner/controller audit to read this axis overlay and rerun PR3148's release. Blocked by: + the release chain has no overlay reader. +- **Can the bit supplier rise toward the new complex root 0.0017347706?** κ is now bit-bound, + so any bit gain up to about +1.34e-6 is realizable. First step: price the actual #589 bit + word with the moment-fee metric and search skip and carrier rewrites on it. + ## Credit - Gonzalo-Mier (PR1252): the move, the rule and the pricing. diff --git a/research/rank7-idle-remainder-donors-t740/SOURCES.json b/research/rank7-idle-remainder-donors-t740/SOURCES.json new file mode 100644 index 0000000000..b6bd6d61d4 --- /dev/null +++ b/research/rank7-idle-remainder-donors-t740/SOURCES.json @@ -0,0 +1,30 @@ +{ + "schema_version": 1, + "base_commit": "997e6a9ca7b4f95d50e366f61412fd640d72a88a", + "files": [ + { + "path": "docs/research/agent-task-catalog.json", + "usage": "provenance", + "git_blob": "67f085acd86acd7d4e03922d9cf4b26bca66fed5", + "sha256": "47b42433f5a85809a3aadd29c2c339da2c6ed728e4f7762df6b88bccb7874cf0" + }, + { + "path": "certificates/selected-result.json", + "usage": "provenance", + "git_blob": "b1fea0c94436b236cc2b7d41a7be032811b94c81", + "sha256": "bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129" + }, + { + "path": "research/adaptive-kernel-demotion/inputs/DATA-PHASES.json", + "usage": "input", + "git_blob": "d9a4f84211182ca200c081ea061d724c8a2cfb70", + "sha256": "c5916ff312678f12aba403847643fbbc29f643acec60bdf836fa56cd3e8251fa" + }, + { + "path": "research/frontier1094-idle-star-ceiling/README.md", + "usage": "provenance", + "git_blob": "dc62e4569948a9e10bb1c72731a9ddfdc81fe0cd", + "sha256": "2f640127f48be627f10a8db1d224d8a75219772525b3c0d5d3251dc8dc57b121" + } + ] +} diff --git a/research/rank7-idle-remainder-donors-t740/TASK.json b/research/rank7-idle-remainder-donors-t740/TASK.json new file mode 100644 index 0000000000..4fabb8702b --- /dev/null +++ b/research/rank7-idle-remainder-donors-t740/TASK.json @@ -0,0 +1,78 @@ +{ + "schema_version": 1, + "task_id": "selected-packing", + "priority_revision": 6, + "base_commit": "997e6a9ca7b4f95d50e366f61412fd640d72a88a", + "original_card": { + "id": "selected-packing", + "question": "Is there a genuinely unsearched, explicitly bounded improvement to the selected packing?", + "starting_points": [ + "certificates/selected-result.json", + "research/heterogeneous-owner-assembly/README.md", + "research/complex-local-word-ceiling/README.md" + ], + "methods": [ + "Search a named unclaimed canonical candidate domain with a reproducible partition.", + "Prove a stronger scoped relaxation or exact optimum for one named residual subproblem." + ], + "acceptance_gate": "Check live PR overlap first, price both suppliers and distinguish a search best from an optimum. Report the word's packing cap from ceiling.ceiling() and the fraction of it realized; label packing gains as such.", + "first_step": { + "command": [ + "python3", + "-B", + "scripts/research_baseline.py" + ], + "expected": "PASS_RESEARCH_BASELINE_BINDINGS_ONLY", + "inspect": "Locate the selected packing source in the review and check live PRs for the same residual problem.", + "scope": "Positive control / source-bound orientation only; this is not a new construction or full cold replay." + }, + "first_experiment": "Define an unclaimed canonical domain and a favorable bound before starting a new search.", + "bottleneck_link": "An actual paid-profile gain can improve the frontier up to the other supplier cap.", + "allowed_variations": [ + "One bounded residual packing instance or exact relaxation.", + "If the coverage law, template or guard changes, derive an applicable fully charged replacement bound instead of applying the incumbent ceiling outside its scope." + ], + "scope_change_triggers": [ + "Rerunning an existing search with only a different seed as a separate mathematical contribution." + ], + "overlap_terms": [ + "T16", + "owner exchange", + "packing" + ], + "existing_checks": [ + { + "scope": "Packing-independent ceiling for the selected paid profile under the one-unpaid-coordinate coverage and halving guard.", + "evidence": "docs/research/community-efficient1000-review.md", + "remaining": "A changed word or model requires new pricing; a local packing search must name uncovered scope.", + "status": "reviewed", + "source_commit": "836b19bfa309ceafbc8ee32a15e8c4b10dde7e11", + "selected_record_sha256": "bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129" + } + ] + }, + "scope_status": "changed", + "actual_scope": "Changed residual subproblem on the open PR3148 T740 fill of PR3133's words (not the selected #1094 packing): idle remainders of partially hosted and fully idle bins donate axes under PR1252's commuting rule to unhosted idle children of the same (replica, port), receivers capped at rank 51, followed by PR3184's star optimum.", + "scope_change_reason": "The card targets the selected packing; this applies the same idle-repartition mechanism (PR1252 / frontier1094-idle-star-ceiling) to the open rank-seven T740 line, whose relaxation cap charges one idle child per bin.", + "bottleneck_link": "Repartitioning idle children changes the paid histogram and so moves the exact complex endpoint.", + "budget_minutes": 120, + "stop_rule": "Stop after the exact overlay, pricing and an independent structural verifier; no controller/outer admission in this session.", + "outcome": "partial", + "evidence": "RESULT.json, BINS.json.gz, MOVES.json.gz (391,964 axis moves), AUDIT.json (8/8 controls rejected).", + "author": "Rohan Arun", + "ai_assistance": "Substantial Anthropic Claude (Claude Code) assistance; idea seeded with help from OpenCode (Space bunny free).", + "open_questions": [ + { + "question": "Is a hosted bin's idle remainder a legal donor under the T74 controller contract?", + "why_it_matters": "PR1252's admitted audit covered only unhosted children; this package relies on orthogonality to the hosted prefix plus the commuting rule.", + "first_step": "Generalize the T74 audit_mixed.py owner/controller audit to read the axis overlay and rerun its controls on PR3148's release.", + "blocked_by": "The T74 release chain has no idle-axis overlay reader." + }, + { + "question": "Can the bit supplier rise toward the new complex root 0.0017347706?", + "why_it_matters": "kappa is now bit-bound; any bit gain up to about +1.34e-6 is realizable.", + "first_step": "Price the actual #589 bit word with the moment-fee metric and search skip/carrier rewrites on it.", + "blocked_by": "Bit word rewrite tooling." + } + ] +} diff --git a/research/rank7-idle-remainder-donors-t740/VERIFY.json b/research/rank7-idle-remainder-donors-t740/VERIFY.json index ac9bd95d36..6639640214 100644 --- a/research/rank7-idle-remainder-donors-t740/VERIFY.json +++ b/research/rank7-idle-remainder-donors-t740/VERIFY.json @@ -1,11 +1,20 @@ { - "commands": [ - [ - "python3", - "-B", - "research/rank7-idle-remainder-donors-t740/verify.py" + "schema_version": 1, + "status": "ready", + "python": "3.12", + "requirements": [], + "inputs": [ + "research/adaptive-kernel-demotion/inputs/DATA-PHASES.json" + ], + "commands": [ + { + "argv": [ + "{python}", + "-B", + "{package}/verify.py" + ], + "timeout_seconds": 300, + "checks": "Independent of build.py: donor axes from the donor's own remainder, unhosted receivers, no child both donates and receives, unit/orthogonal-at-receipt and commuting rule, rank cap 51, group multisets, profile and rank mass, exact complex root bracket with its own interval arithmetic, kappa = min(floor24(complex), PR589 bit) - 1e-46 - 1e-70 and gates over PR3148/PR3184; 8 mutation controls rejected." + } ] - ], - "expected": "PASS_IDLE_REMAINDER_DONOR_AUDIT", - "seconds": 70 -} \ No newline at end of file +} diff --git a/research/rank7-idle-remainder-donors-t740/verify.py b/research/rank7-idle-remainder-donors-t740/verify.py index 39343120e2..ca607d6a86 100644 --- a/research/rank7-idle-remainder-donors-t740/verify.py +++ b/research/rank7-idle-remainder-donors-t740/verify.py @@ -117,6 +117,7 @@ def main(): ap = argparse.ArgumentParser(description=__doc__) ap.add_argument('--t740', type=Path) ap.add_argument('--providers', type=Path, default=PKG / 'PR3148-PROVIDERS.json') + ap.add_argument('--write', action='store_true', help='rewrite the committed AUDIT.json receipt') a = ap.parse_args() if not __debug__: raise SystemExit('assertions required') raw = PHASES.read_bytes() @@ -166,7 +167,10 @@ def mut(f): else: raise SystemExit('mutation accepted: kappa_above_bit') out = dict(status='PASS_IDLE_REMAINDER_DONOR_AUDIT', moves=len(mv), fill_rebound=rebound, kappa=str(kappa), complex_root_lower=str(lo), binding='bit' if BIT < lo else 'complex', rejected_controls=rej) - (PKG / 'AUDIT.json').write_text(json.dumps(out, indent=1, sort_keys=True) + '\n') + if a.write: (PKG / 'AUDIT.json').write_text(json.dumps(out, indent=1, sort_keys=True) + '\n') + else: + strip = lambda d: {k: v for k, v in d.items() if k != 'fill_rebound'} + req(strip(load(PKG / 'AUDIT.json')) == strip(json.loads(json.dumps(out))), 'committed AUDIT.json receipt') print('PASS_IDLE_REMAINDER_DONOR_AUDIT moves=%d controls=%d kappa=%s binding=%s' % (len(mv), len(rej), float(kappa), out['binding'])) From 418ea1dc11030a23c1547b4e2b64ef4a46be2881 Mon Sep 17 00:00:00 2001 From: Rohan Arun Date: Sat, 17 Oct 2026 12:52:25 -0400 Subject: [PATCH 3/4] Conditional kappa = 0.001734770557111513160495: R438 bit supplier with PR3190's idle-remainder donors PR3190 pushed the complex root (0.0017347705571115131604951) past the PR589 bit saving. The R438 bit supplier natively replayed on main (0.001734846264120199151475) is above it, so the complex side binds again: +1.3435e-6 over PR3190. Independent re-derivation of both endpoints and the composed kappa; 3 controls rejected. Done with help from OpenCode (Space bunny free). Co-Authored-By: Claude Opus 5.5 Claude-Session: https://claude.ai/code/session_011S35E2acyQDaVRjPRw4TDy --- .../rank7-idle-donors-r438-bit/CLAIM.json | 11 ++ research/rank7-idle-donors-r438-bit/README.md | 87 ++++++++++++++ .../rank7-idle-donors-r438-bit/SOURCES.json | 31 +++++ research/rank7-idle-donors-r438-bit/TASK.json | 72 +++++++++++ .../rank7-idle-donors-r438-bit/VERIFY.json | 21 ++++ research/rank7-idle-donors-r438-bit/verify.py | 113 ++++++++++++++++++ 6 files changed, 335 insertions(+) create mode 100644 research/rank7-idle-donors-r438-bit/CLAIM.json create mode 100644 research/rank7-idle-donors-r438-bit/README.md create mode 100644 research/rank7-idle-donors-r438-bit/SOURCES.json create mode 100644 research/rank7-idle-donors-r438-bit/TASK.json create mode 100644 research/rank7-idle-donors-r438-bit/VERIFY.json create mode 100644 research/rank7-idle-donors-r438-bit/verify.py diff --git a/research/rank7-idle-donors-r438-bit/CLAIM.json b/research/rank7-idle-donors-r438-bit/CLAIM.json new file mode 100644 index 0000000000..ce2245e7a4 --- /dev/null +++ b/research/rank7-idle-donors-r438-bit/CLAIM.json @@ -0,0 +1,11 @@ +{ + "kappa": "17347705571115131604949999999999999999999998999999999999999999999999/10000000000000000000000000000000000000000000000000000000000000000000000", + "kappa_decimal": "0.0017347705571115131604949999999999999999999998999999999999999999999999", + "complex_root": [ + "17347705571115131604951/10000000000000000000000000", + "17347705571115131604952/10000000000000000000000000" + ], + "bit_supplier": "R438 (PR1043 + PR2423, research/r438-native-rehost) 0.001734846264120199151475", + "binding": "complex", + "gain_over_pr3190": "671758760834462873/500000000000000000000000" +} diff --git a/research/rank7-idle-donors-r438-bit/README.md b/research/rank7-idle-donors-r438-bit/README.md new file mode 100644 index 0000000000..09c6859328 --- /dev/null +++ b/research/rank7-idle-donors-r438-bit/README.md @@ -0,0 +1,87 @@ +# R438 bit supplier with PR3190's idle-remainder donors: the complex side binds again at κ = 0.001734770557111513160495 − 10⁻⁴⁶ − 10⁻⁷⁰ + +**Author-checked conditional composition; not maintainer-reviewed.** The selected record on +`main` is still #1094. This package stacks on the open PR3190 +(`research/rank7-idle-remainder-donors-t740`). + +| | complex endpoint | bit endpoint | binds | κ headline | +|---|---|---|---|---| +| PR3190 | 0.0017347705571115131604951 | PR589 0.001733427039589844234749 | bit | 0.001733427039589844234749 − … | +| **this** | 0.0017347705571115131604951 | **R438 0.001734846264120199151475** | **complex** | **0.001734770557111513160495 − 10⁻⁴⁶ − 10⁻⁷⁰** | + +The gain is **+1.3435e-6 (+0.0775%) over PR3190**, +4.58e-6 over PR3184 and +4.99e-6 over +PR3148. + +## Idea + +PR3190's idle-remainder exchanges pushed the complex root of PR3133's words above the PR589 bit +saving, so its κ was capped by the bit supplier. A stronger certified bit supplier already exists on +main. + +The R438 word: + +- comes from Ali Romman's PR1043, with helper 470 deleted; +- adds Sagar Thakrar's PR2423 transport and optimal re-hosting; +- has a complete native, parent and hosted replay in `research/r438-native-rehost`. + +Its bit endpoint is 0.001734846264120199151475, accepted at c and rejected at c + 10⁻²⁴. That is +above the new complex root, so with R438 the complex side binds again. + +## Verification + +`verify.py` uses the standard library only and runs in about 1 s: + +1. **Complex endpoint.** It recomputes PR3190's complex root bracket on its declared complete + profile, with its own interval arithmetic at 10⁻⁷². +2. **Bit endpoint.** It re-derives the R438 endpoint from the certificate's own bit profile: + m = 64, live = 28,416, with the 10⁻¹⁶·32m² bad-edge fallback envelope. The endpoint is accepted + at c and rejected at c + 10⁻²⁴. +3. **Composed κ.** It computes `κ = min(floor₂₄(complex), floor₂₄(bit)) − 10⁻⁴⁶ − 10⁻⁷⁰`, checks it + equals CLAIM.json, and gates it against PR3148, PR3184 and PR3190. + +Three mutation controls are rejected: the complex next grid point, the bit next grid point, and +the PR589 endpoint on the R438 profile. PR3190's moves and profile are checked by its own +registered verifier. + +```sh +python3 -B research/rank7-idle-donors-r438-bit/verify.py +``` + +## Scope + +**Conditional on two unreviewed claims:** + +- PR3190 and its stack: PR3148, PR3133, and the hosted-remainder donor hypothesis. +- R438: PR1043 is open, and `r438-native-rehost` does not promote a selected supplier. + +The R438 bill fits the inherited row bound: row coefficient 18,355 < 20,161, maxchild 42 with +`2·42² < 64²`. + +The T74 outer ledger currently pins the PR589 bit constant, and only uses it to assert +`complex < bit`. With R438 that assertion holds directly, but the release needs the constant +re-pinned. All inherited all-size, compiler, realization, precision and analytic obligations +remain. + +## Open next questions + +- **Does the T74 outer release accept R438 in place of PR589?** First step: rerun PR3148's outer + release with the R438 bit endpoint and its finite bill. Blocked by: PR1043 is open, and the outer + ledger pins PR589. +- **Can the complex side close the remaining 7.6e-8 gap to the R438 endpoint?** First step: drain + more of the 149,514 rank-1 remainders that are blocked by commuting legality, or widen the + receiver set. +- **Bit side.** R438's own idle remainder (`{34:32, 42:320}`, cap 45 at m = 64) admits the same + axis-exchange question, should the bit side bind again. + +## Credit + +- Ali Romman (PR1043): the R438 word. +- Sagar Thakrar (PR2423): transport and re-hosting. +- commdata2338 (PR2653): native emission. +- The `r438-native-rehost` authors. +- PR3190 / PR3184 and their credits: PR1252 Gonzalo-Mier; Guéorgui Maissouradze; PR3148 Jeremy + Diviney; PR3133 dcharb78; PR2979 Marius-Paul Dumitrean. +- DreamingOfClouds and eumemic (PR589/PR555). + +Prepared by Rohan Arun. Done with help from **OpenCode (Space bunny free)**, and with Anthropic +Claude assistance. Apache-2.0. diff --git a/research/rank7-idle-donors-r438-bit/SOURCES.json b/research/rank7-idle-donors-r438-bit/SOURCES.json new file mode 100644 index 0000000000..16e857fa25 --- /dev/null +++ b/research/rank7-idle-donors-r438-bit/SOURCES.json @@ -0,0 +1,31 @@ +{ + "schema_version": 1, + "base_commit": "997e6a9ca7b4f95d50e366f61412fd640d72a88a", + "files": [ + { + "path": "docs/research/agent-task-catalog.json", + "usage": "provenance", + "git_blob": "67f085acd86acd7d4e03922d9cf4b26bca66fed5", + "sha256": "47b42433f5a85809a3aadd29c2c339da2c6ed728e4f7762df6b88bccb7874cf0" + }, + { + "path": "certificates/selected-result.json", + "usage": "provenance", + "git_blob": "b1fea0c94436b236cc2b7d41a7be032811b94c81", + "sha256": "bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129" + }, + { + "path": "research/r438-native-rehost/CERTIFICATE.json", + "usage": "input", + "git_blob": "674ef36f723fbcc593e7d2319dca131da09181e5", + "sha256": "6da8c593257c8440f0fe35488d941715d953d715e2e464ffdfffff7ed31eee9c" + }, + { + "path": "research/rank7-idle-remainder-donors-t740/RESULT.json", + "usage": "input", + "git_blob": "2bbb2926bbd892129e988c962bc71632e42b2094", + "sha256": "3380908be142237abead45abddfb28c8a8804b61496040e8a8a8c5ef5edc5dc9", + "pin": "head:5e4a3235169edddd033889da4e9f47635ff50c3e:research/rank7-idle-remainder-donors-t740/RESULT.json" + } + ] +} diff --git a/research/rank7-idle-donors-r438-bit/TASK.json b/research/rank7-idle-donors-r438-bit/TASK.json new file mode 100644 index 0000000000..0611ef7283 --- /dev/null +++ b/research/rank7-idle-donors-r438-bit/TASK.json @@ -0,0 +1,72 @@ +{ + "schema_version": 1, + "task_id": "independent-moment", + "priority_revision": 6, + "base_commit": "997e6a9ca7b4f95d50e366f61412fd640d72a88a", + "original_card": { + "id": "independent-moment", + "question": "Does one changed supplier or assembly claim lack a source-bound independent check of a specific new implication?", + "starting_points": [ + "certificates/selected-result.json", + "research/rank7-joint-endframes/README.md", + "docs/research/research-family-status.md" + ], + "methods": [ + "Independently reconstruct a coordinated frame/circuit change and its single-change control, then derive the complete rank and physical ledger.", + "Implement certified moment inequalities through a different exact enclosure method." + ], + "acceptance_gate": "Demonstrate independence, source binding, positive cases and semantic failure controls. Name the existing checks and the missing coverage. More digits or another equivalent evaluation of an unchanged root is not by itself new verification coverage.", + "first_step": { + "command": [ + "python3", + "-B", + "scripts/research_baseline.py" + ], + "expected": "PASS_RESEARCH_BASELINE_BINDINGS_ONLY", + "inspect": "Read #2979 joint rank-7 end-frame proposal and the revision-6 evidence status. Its claimed kappa is not selected. Compare coordinated changes with the losing single-change controls and locate the complete physical ledger; an aggregate moment alone does not validate the mechanism.", + "scope": "Positive control / source-bound orientation only; this is not a new construction or full cold replay." + }, + "first_experiment": "Prioritize a bounded independent audit of #2979: reconstruct one joint group and its single-lowering control, check the declared frames/chronology, then trace changed children, idle widths and cleanup buffers into the complete invoice and both supplier caps. Choose one still-missing implication after checking existing audits. Stop with exact unresolved dependencies if full admission exceeds the session; do not launch a new lowering census on an unvalidated premise or substitute extra root digits for mechanism checking.", + "bottleneck_link": "Independent pricing prevents unsupported frontier claims and can reveal genuine accounting slack.", + "allowed_variations": [ + "Reconstruct either a source ledger or a numeric enclosure with a different method." + ], + "scope_change_triggers": [ + "Importing the primary function and calling its output independent verification.", + "Promoting #2979 from merged source archive to validated supplier solely from author PASS receipts or aggregate pricing." + ], + "overlap_terms": [ + "independent moment", + "rank histogram", + "exact enclosure", + "2979", + "rank7 joint endframes", + "paired extraction", + "joint lowering" + ] + }, + "scope_status": "changed", + "actual_scope": "Supplier composition: PR3190's idle-remainder complex endpoint for PR3133's words on PR3148's T740 fill (0.0017347705571115131604951) with the R438 bit supplier natively replayed on main (research/r438-native-rehost, 0.001734846264120199151475). Independent re-derivation of both endpoints and of the composed kappa.", + "scope_change_reason": "PR3190 made the complex side exceed the PR589 bit saving, so the useful next check is which certified bit supplier binds; R438 is above the new complex root.", + "bottleneck_link": "kappa = min(complex, bit) minus slacks; swapping in the stronger R438 bit supplier lets the complex side bind again.", + "budget_minutes": 45, + "stop_rule": "Stop after independent endpoint checks and the composed kappa; no new construction.", + "outcome": "partial", + "evidence": "verify.py: complex root bracket recomputed, R438 bit endpoint accepted at c and rejected at c+1e-24 (with fallback envelope), kappa gates; 3 mutation controls rejected.", + "author": "Rohan Arun", + "ai_assistance": "Substantial Anthropic Claude (Claude Code) assistance; done with help from OpenCode (Space bunny free).", + "open_questions": [ + { + "question": "Is R438 (conditional on open PR1043) compatible with the rank-seven T74 outer release when substituted for PR589?", + "why_it_matters": "The composed kappa needs the outer ledger to accept the R438 bit row bill (row coefficient 18,355 < 20,161).", + "first_step": "Rerun PR3148's outer release with the R438 bit endpoint and its finite bill.", + "blocked_by": "PR1043 is open; the T74 outer pins the PR589 bit constant." + }, + { + "question": "Can the complex side be pushed the remaining 7.6e-8 to the R438 bit endpoint?", + "why_it_matters": "Beyond that the bit side binds again.", + "first_step": "Drain more of the 149,514 rank-1 remainders (legality-blocked) or extend receivers.", + "blocked_by": "Commuting-rule legality." + } + ] +} diff --git a/research/rank7-idle-donors-r438-bit/VERIFY.json b/research/rank7-idle-donors-r438-bit/VERIFY.json new file mode 100644 index 0000000000..53473318eb --- /dev/null +++ b/research/rank7-idle-donors-r438-bit/VERIFY.json @@ -0,0 +1,21 @@ +{ + "schema_version": 1, + "status": "ready", + "python": "3.12", + "requirements": [], + "inputs": [ + "research/r438-native-rehost/CERTIFICATE.json", + "research/rank7-idle-remainder-donors-t740/RESULT.json" + ], + "commands": [ + { + "argv": [ + "{python}", + "-B", + "{package}/verify.py" + ], + "timeout_seconds": 120, + "checks": "Recomputes PR3190 complex root bracket and the R438 bit endpoint (accept at c, reject at c+1e-24, fallback envelope) with its own interval arithmetic; kappa = min(floor24(complex), floor24(bit)) - 1e-46 - 1e-70 equals CLAIM.json and exceeds PR3148/PR3184/PR3190; 3 mutation controls rejected." + } + ] +} diff --git a/research/rank7-idle-donors-r438-bit/verify.py b/research/rank7-idle-donors-r438-bit/verify.py new file mode 100644 index 0000000000..a75737fbe3 --- /dev/null +++ b/research/rank7-idle-donors-r438-bit/verify.py @@ -0,0 +1,113 @@ +#!/usr/bin/env python3 +# SPDX-License-Identifier: Apache-2.0 +"""Compose the PR3190 idle-remainder complex endpoint with the R438 bit supplier. + +PR3190 (research/rank7-idle-remainder-donors-t740) raised the complex root of PR3133's words on +PR3148's T740 fill to 0.0017347705571115131604951, past the PR589 bit saving, so its kappa was +bit-capped at 0.001733427039589844234749. The R438 bit supplier (PR1043 word, PR2423 transport and +re-hosting, natively replayed in research/r438-native-rehost on main) has bit endpoint +0.001734846264120199151475, above that complex root. With it the complex side binds again. + +This verifier (standard library only): + 1. re-derives the complex root bracket of PR3190's declared profile with its own interval arithmetic; + 2. re-derives the R438 bit endpoint from the certificate's own bit profile (m = 64, live = 28,416, + with the 10^-16 * 32 m^2 fallback envelope): accepted at c, rejected at c + 1e-24; + 3. computes kappa = min(floor24(complex_lower), floor24(bit_lower)) - 1e-46 - 1e-70 and gates it. +The moves and profile of PR3190 are checked by that package's own registered verifier. +""" +import argparse, hashlib, json +from fractions import Fraction as F +from pathlib import Path + +PKG = Path(__file__).resolve().parent +ROOT = PKG.parents[1] +COMPLEX = ROOT / 'research/rank7-idle-remainder-donors-t740/RESULT.json' +BITCERT = ROOT / 'research/r438-native-rehost/CERTIFICATE.json' +GATES = dict(PR3148=F('0.0017297774946785970118859999999999999999999998999999999999999999999999'), + PR3184=F('0.0017301890612338507600949999999999999999999998999999999999999999999999'), + PR3190=F('0.0017334270395898442347489999999999999999999998999999999999999999999999')) + + +class Reject(Exception): pass +def req(ok, why): + if not ok: raise Reject(why) + +Q72 = 10 ** 72 +def rd(x): return F(x.numerator * Q72 // x.denominator, Q72) +def ru(x): return F(-((-x.numerator * Q72) // x.denominator), Q72) +def atanh2(z, n): + s, p = F(0), z + for j in range(n): s += p / (2 * j + 1); p *= z * z + return 2 * s, 2 * p / ((2 * n + 1) * (1 - z * z)) +L2 = atanh2(F(1, 3), 130) +def ln_box(y): + k = 0 + while y >= 2: y /= 2; k += 1 + a, e = atanh2((y - 1) / (y + 1), 90) + return rd(a + k * L2[0]), ru(a + e + k * (L2[0] + L2[1])) +def exp_box(x0, x1): + def tay(x): + s, t = F(1), F(1) + for j in range(1, 34): t = t * x / j; s += t + return s, t * x / 34 * 3 + a, _ = tay(x0); b, t = tay(x1) + return rd(a), ru(b + t) +def moment(prof, m, W, b, bad=False): + lo = hi = F(0) + items = sorted(prof.items()) + if bad: # bad-edge Gaussian fallback envelope, 10^-16 * 32 m^2 rank-1 children per child (bit pricing) + items = items + [(1, F(32 * m * m * sum(prof.values()), 10 ** 16))] + for r, n in items: + l0, l1 = ln_box(F(m, r)); e0, e1 = exp_box(b * l0, b * l1) + lo += n * r * e0; hi += n * r * e1 + return lo / (m * W), hi / (m * W) + + +def compose(cx, bit): + prof = {int(k): v for k, v in cx['profile'].items()} + req(sum(r * n for r, n in prof.items()) == 65088 * 740 and max(prof) <= 51, 'PR3190 profile mass/halving') + lo, hi = F(cx['complex_root'][0]), F(cx['complex_root'][1]) + req(hi - lo == F(1, 10 ** 25) and moment(prof, 73, 896 * 740, lo)[1] < 1 < moment(prof, 73, 896 * 740, hi)[0], 'complex root bracket') + inv = bit['pipeline']['candidate']['hosted']['invoice'] + bprof = {int(k): v for k, v in json.loads(inv['bit_profile'].replace("'", '"')).items()} if isinstance(inv['bit_profile'], str) else {int(k): v for k, v in inv['bit_profile'].items()} + c = F(inv['bit_lower']); c_next = F(inv['next_grid_point_rejected']) + req(c == F(inv['bit_lower_decimal']) and c_next - c == F(1, 10 ** 24), 'bit certificate fields') + W = 28416 + req(64 * W - sum(r * n for r, n in bprof.items()) > 0 and 2 * max(bprof) ** 2 < 64 ** 2, 'bit profile deficit/halving') + req(moment(bprof, 64, W, c, True)[1] < 1 and moment(bprof, 64, W, c_next, True)[0] > 1, 'bit endpoint accepted at c, rejected at c+1e-24') + floor24 = lambda x: F(x.numerator * 10 ** 24 // x.denominator, 10 ** 24) + C = min(floor24(lo), floor24(c)) + req(C == floor24(lo) and floor24(lo) < c, 'complex binds below the R438 bit endpoint') + kappa = C - F(1, 10 ** 46) - F(1, 10 ** 70) + for n, g in GATES.items(): req(kappa > g, 'kappa must exceed ' + n) + return kappa, lo, c + + +def main(): + ap = argparse.ArgumentParser(description=__doc__); ap.parse_args() + if not __debug__: raise SystemExit('assertions required') + cx = json.loads(COMPLEX.read_text()); bit = json.loads(BITCERT.read_text()) + claim = json.loads((PKG / 'CLAIM.json').read_text()) + kappa, lo, c = compose(cx, bit) + req(F(claim['kappa']) == kappa == F(claim['kappa_decimal']), 'CLAIM kappa') + rej = {} + import copy + for name, mut in [('complex_next_grid', lambda x, b: x.__setitem__('complex_root', [str(lo + F(1, 10**25)), str(lo + F(2, 10**25))])), + ('bit_next_grid', lambda x, b: b['pipeline']['candidate']['hosted']['invoice'].update( + bit_lower=str(F(b['pipeline']['candidate']['hosted']['invoice']['next_grid_point_rejected'])), + bit_lower_decimal=str(F(b['pipeline']['candidate']['hosted']['invoice']['next_grid_point_rejected'])), + next_grid_point_rejected=str(F(b['pipeline']['candidate']['hosted']['invoice']['next_grid_point_rejected']) + F(1, 10**24)))), + ('pr589_bit', lambda x, b: b['pipeline']['candidate']['hosted']['invoice'].update( + bit_lower='1733427039589844234749/1000000000000000000000000', bit_lower_decimal='1733427039589844234749/1000000000000000000000000', + next_grid_point_rejected='1733427039589844234750/1000000000000000000000000'))]: + x, b = copy.deepcopy(cx), copy.deepcopy(bit); mut(x, b) + try: compose(x, b) + except Reject as e: rej[name] = str(e) + else: raise SystemExit('mutation accepted: ' + name) + print('PASS_R438_COMPOSITION kappa=%s complex=%s bit=%s controls=%d' % (float(kappa), float(lo), float(c), len(rej))) + print(json.dumps(rej, sort_keys=True)) + + +if __name__ == '__main__': + try: main() + except Reject as e: raise SystemExit('FAIL: ' + str(e)) From f09e5b25381393c604082e58fbe56896b13171b5 Mon Sep 17 00:00:00 2001 From: Rohan Arun Date: Sat, 17 Oct 2026 13:10:31 -0400 Subject: [PATCH 4/4] Conditional kappa = 0.001734807021726127552033: greedy idle-axis phase on PR3198 (R438 bit) Adds a third phase of single-axis PR1252-rule moves between unhosted idle children to PR3190's remainder donors and PR3184's stars: 430,164 moves, complex root 0.0017348070217261275520343, still below the R438 bit endpoint. +3.646e-8 over PR3198. Independent verifier re-derives the moves, the complex bracket and the R438 endpoint; 8 controls rejected. Done with help from OpenCode (Space bunny free). Co-Authored-By: Claude Opus 5.5 Claude-Session: https://claude.ai/code/session_011S35E2acyQDaVRjPRw4TDy --- .../rank7-idle-donors-greedy-r438/AUDIT.json | 18 + .../BINS.json.gz | Bin 0 -> 239829 bytes .../rank7-idle-donors-greedy-r438/CLAIM.json | 31 + .../MOVES.json.gz | Bin 0 -> 1306990 bytes .../PR3148-PROVIDERS.json | 842 ++++++++++++++++++ .../rank7-idle-donors-greedy-r438/README.md | 104 +++ .../rank7-idle-donors-greedy-r438/RESULT.json | 62 ++ .../SOURCES.json | 30 + .../rank7-idle-donors-greedy-r438/TASK.json | 78 ++ .../rank7-idle-donors-greedy-r438/VERIFY.json | 21 + .../rank7-idle-donors-greedy-r438/build.py | 226 +++++ .../rank7-idle-donors-greedy-r438/verify.py | 219 +++++ 12 files changed, 1631 insertions(+) create mode 100644 research/rank7-idle-donors-greedy-r438/AUDIT.json create mode 100644 research/rank7-idle-donors-greedy-r438/BINS.json.gz create mode 100644 research/rank7-idle-donors-greedy-r438/CLAIM.json create mode 100644 research/rank7-idle-donors-greedy-r438/MOVES.json.gz create mode 100644 research/rank7-idle-donors-greedy-r438/PR3148-PROVIDERS.json create mode 100644 research/rank7-idle-donors-greedy-r438/README.md create mode 100644 research/rank7-idle-donors-greedy-r438/RESULT.json create mode 100644 research/rank7-idle-donors-greedy-r438/SOURCES.json create mode 100644 research/rank7-idle-donors-greedy-r438/TASK.json create mode 100644 research/rank7-idle-donors-greedy-r438/VERIFY.json create mode 100644 research/rank7-idle-donors-greedy-r438/build.py create mode 100644 research/rank7-idle-donors-greedy-r438/verify.py diff --git a/research/rank7-idle-donors-greedy-r438/AUDIT.json b/research/rank7-idle-donors-greedy-r438/AUDIT.json new file mode 100644 index 0000000000..83457354ff --- /dev/null +++ b/research/rank7-idle-donors-greedy-r438/AUDIT.json @@ -0,0 +1,18 @@ +{ + "binding": "complex", + "complex_root_lower": "2168508777157659440043/1250000000000000000000000", + "fill_rebound": true, + "kappa": "17348070217261275520339999999999999999999998999999999999999999999999/10000000000000000000000000000000000000000000000000000000000000000000000", + "moves": 430164, + "rejected_controls": { + "axis_moved_twice": "axis not in donor remainder", + "dropped_move": "declared profile", + "foreign_axis": "axis not in donor remainder", + "hosted_axis_from_used_prefix": "axis not in donor remainder", + "hosted_receiver": "receiver must be unhosted", + "kappa_above_bit": "headline kappa", + "next_root_grid": "complex root bracket", + "receiver_donates": "receiver must be unhosted" + }, + "status": "PASS_IDLE_DONOR_GREEDY_R438_AUDIT" +} diff --git a/research/rank7-idle-donors-greedy-r438/BINS.json.gz b/research/rank7-idle-donors-greedy-r438/BINS.json.gz new file mode 100644 index 0000000000000000000000000000000000000000..fc2446437c8ba8b5f10aa4cefd5290927c64dc26 GIT binary patch literal 239829 zcmd431z1$w->8jJgLFtYQc6ln3J6Gts0auWQqm&Q2n-=1Qi60yS%83~zznT4DBUeJ 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research/rank7-idle-donors-greedy-r438/verify.py --t740 /tmp/t740 # ~70 s +``` + +`verify.py` does not import `build.py`. It re-derives: + +- every move's donor-remainder membership, receiver hosting status, roles and the commuting rule; +- the rank cap; +- the profile and rank mass; +- the exact complex root bracket; +- the R438 bit endpoint, from its certificate's own bit profile with the fallback envelope + (accepted at c, rejected at c + 10⁻²⁴); +- `κ = min(floor₂₄(complex), bit) − 10⁻⁴⁶ − 10⁻⁷⁰`, checking that the complex side binds; +- the gates over PR3148, PR3184 and PR3198. + +Eight mutation controls are rejected. The run checks against the committed `AUDIT.json` without +writing to it. + +## Scope + +This is conditional on PR3198's stack: PR3190, PR3184, PR3148 and PR3133. It is also conditional +on R438, whose source PR1043 is open. + +The hosted-remainder donor hypothesis and the greedy single-axis chains (a child receiving from +several donors) rely on PR1252's per-axis rule. Only unhosted pairs have an admitted controller +audit. The native admission, the overlay-aware controller audit and the outer release were not +rerun. All inherited obligations remain. + +## Open next questions + +- **Do hosted donors and multi-donor receivers satisfy the T74 controller contract?** First step: + generalize the T74 `audit_mixed.py` to read the idle-axis overlay. Blocked by: the T74 chain has + no overlay reader. +- **Can the remaining 3.9e-8 to R438 be closed, and can R438 itself rise?** First step: exact + per-group optimisation instead of greedy, and idle exchanges on R438's own + `{34:32, 42:320}` remainders. Blocked by: the cost of the per-group search, and R438's per-child + axis data. + +## Credit + +- PR1252 (Gonzalo-Mier): the move, the rule and the pricing. +- Guéorgui Maissouradze: the star class. +- PR3148 (Jeremy Diviney): the fill. +- PR3133 and PR3042 (dcharb78): the words. +- PR2979 (Marius-Paul Dumitrean). +- Ali Romman (PR1043) and Sagar Thakrar (PR2423): R438. +- The `r438-native-rehost` authors. +- DreamingOfClouds and eumemic. + +Prepared by Rohan Arun. Done with help from **OpenCode (Space bunny free)**, with Anthropic +Claude assistance. Apache-2.0. diff --git a/research/rank7-idle-donors-greedy-r438/RESULT.json b/research/rank7-idle-donors-greedy-r438/RESULT.json new file mode 100644 index 0000000000..3b6d80114e --- /dev/null +++ b/research/rank7-idle-donors-greedy-r438/RESULT.json @@ -0,0 +1,62 @@ +{ + "status": "PASS_IDLE_DONOR_GREEDY_R438_T740", + "T": 740, + "axis_moves": 430164, + "donor_children": 151509, + "receiver_children": 167112, + "idle_before": { + "1": 173160, + "3": 48951, + "5": 13875, + "48": 282569 + }, + "idle_after": { + "1": 149514, + "2": 15880, + "3": 14951, + "5": 13855, + "42": 32303, + "44": 5120, + "45": 36420, + "46": 6300, + "47": 20, + "48": 35294, + "49": 28786, + "50": 13600, + "51": 124726 + }, + "profile": { + "1": 16353294, + "2": 4837720, + "3": 1533431, + "4": 679320, + "5": 147055, + "8": 53280, + "42": 32303, + "44": 5120, + "45": 36420, + "46": 6300, + "47": 20, + "48": 35294, + "49": 28786, + "50": 13600, + "51": 124726 + }, + "complex_root": [ + "2168508777157659440043/1250000000000000000000000", + "3469614043452255104069/2000000000000000000000000" + ], + "complex_root_decimal": "17348070217261275520344e-25", + "bit": "69393850564807966059/40000000000000000000000", + "binding": "complex", + "kappa": "17348070217261275520339999999999999999999998999999999999999999999999/10000000000000000000000000000000000000000000000000000000000000000000000", + "kappa_decimal": "0.0017348070217261275520339999999999999999999998999999999999999999999999", + "gain_over_pr3198": "36464614614391539/1000000000000000000000000", + "gain_over_pr3184": "4617960492276791939/1000000000000000000000000", + "gain_over_pr3148": "1257381761882635037/250000000000000000000000", + "max_child_rank": 51, + "halving": [ + 5329, + 5202 + ] +} diff --git a/research/rank7-idle-donors-greedy-r438/SOURCES.json b/research/rank7-idle-donors-greedy-r438/SOURCES.json new file mode 100644 index 0000000000..bb4884cb26 --- /dev/null +++ b/research/rank7-idle-donors-greedy-r438/SOURCES.json @@ -0,0 +1,30 @@ +{ + "schema_version": 1, + "base_commit": "997e6a9ca7b4f95d50e366f61412fd640d72a88a", + "files": [ + { + "path": "docs/research/agent-task-catalog.json", + "usage": "provenance", + "git_blob": "67f085acd86acd7d4e03922d9cf4b26bca66fed5", + "sha256": "47b42433f5a85809a3aadd29c2c339da2c6ed728e4f7762df6b88bccb7874cf0" + }, + { + "path": "certificates/selected-result.json", + "usage": "provenance", + "git_blob": "b1fea0c94436b236cc2b7d41a7be032811b94c81", + "sha256": "bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129" + }, + { + "path": "research/adaptive-kernel-demotion/inputs/DATA-PHASES.json", + "usage": "input", + "git_blob": "d9a4f84211182ca200c081ea061d724c8a2cfb70", + "sha256": "c5916ff312678f12aba403847643fbbc29f643acec60bdf836fa56cd3e8251fa" + }, + { + "path": "research/r438-native-rehost/CERTIFICATE.json", + "usage": "input", + "git_blob": "674ef36f723fbcc593e7d2319dca131da09181e5", + "sha256": "6da8c593257c8440f0fe35488d941715d953d715e2e464ffdfffff7ed31eee9c" + } + ] +} diff --git a/research/rank7-idle-donors-greedy-r438/TASK.json b/research/rank7-idle-donors-greedy-r438/TASK.json new file mode 100644 index 0000000000..0922e82be5 --- /dev/null +++ b/research/rank7-idle-donors-greedy-r438/TASK.json @@ -0,0 +1,78 @@ +{ + "schema_version": 1, + "task_id": "selected-packing", + "priority_revision": 6, + "base_commit": "997e6a9ca7b4f95d50e366f61412fd640d72a88a", + "original_card": { + "id": "selected-packing", + "question": "Is there a genuinely unsearched, explicitly bounded improvement to the selected packing?", + "starting_points": [ + "certificates/selected-result.json", + "research/heterogeneous-owner-assembly/README.md", + "research/complex-local-word-ceiling/README.md" + ], + "methods": [ + "Search a named unclaimed canonical candidate domain with a reproducible partition.", + "Prove a stronger scoped relaxation or exact optimum for one named residual subproblem." + ], + "acceptance_gate": "Check live PR overlap first, price both suppliers and distinguish a search best from an optimum. Report the word's packing cap from ceiling.ceiling() and the fraction of it realized; label packing gains as such.", + "first_step": { + "command": [ + "python3", + "-B", + "scripts/research_baseline.py" + ], + "expected": "PASS_RESEARCH_BASELINE_BINDINGS_ONLY", + "inspect": "Locate the selected packing source in the review and check live PRs for the same residual problem.", + "scope": "Positive control / source-bound orientation only; this is not a new construction or full cold replay." + }, + "first_experiment": "Define an unclaimed canonical domain and a favorable bound before starting a new search.", + "bottleneck_link": "An actual paid-profile gain can improve the frontier up to the other supplier cap.", + "allowed_variations": [ + "One bounded residual packing instance or exact relaxation.", + "If the coverage law, template or guard changes, derive an applicable fully charged replacement bound instead of applying the incumbent ceiling outside its scope." + ], + "scope_change_triggers": [ + "Rerunning an existing search with only a different seed as a separate mathematical contribution." + ], + "overlap_terms": [ + "T16", + "owner exchange", + "packing" + ], + "existing_checks": [ + { + "scope": "Packing-independent ceiling for the selected paid profile under the one-unpaid-coordinate coverage and halving guard.", + "evidence": "docs/research/community-efficient1000-review.md", + "remaining": "A changed word or model requires new pricing; a local packing search must name uncovered scope.", + "status": "reviewed", + "source_commit": "836b19bfa309ceafbc8ee32a15e8c4b10dde7e11", + "selected_record_sha256": "bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129" + } + ] + }, + "scope_status": "changed", + "actual_scope": "Changed residual subproblem on the open PR3148 T740 fill of PR3133's words: PR3190's idle-remainder donors and PR3184's stars, plus a third greedy phase of single-axis PR1252-rule moves between unhosted idle children (smaller to equal-or-larger, cap 51), composed with the R438 bit supplier (research/r438-native-rehost).", + "scope_change_reason": "PR3198 left the complex side binding 7.6e-8 below the R438 bit endpoint; this closes about half of that window with more legal idle moves.", + "bottleneck_link": "kappa = min(complex, bit); the complex side binds, and more idle repartition lowers its moment cost.", + "budget_minutes": 60, + "stop_rule": "Stop after the exact overlay, pricing and independent verifier; no controller/outer admission.", + "outcome": "partial", + "evidence": "RESULT.json, BINS.json.gz, MOVES.json.gz (430,164 axis moves), AUDIT.json (8/8 controls rejected), R438 endpoint re-derived.", + "author": "Rohan Arun", + "ai_assistance": "Substantial Anthropic Claude (Claude Code) assistance; done with help from OpenCode (Space bunny free).", + "open_questions": [ + { + "question": "Are hosted remainders legal donors and do greedy chains of single-axis moves satisfy the T74 controller contract?", + "why_it_matters": "Only PR1252 unhosted pairs have an admitted controller audit.", + "first_step": "Generalize the T74 audit_mixed.py to read the idle-axis overlay and rerun PR3148's release.", + "blocked_by": "No overlay reader in the T74 chain." + }, + { + "question": "Can the remaining 3.9e-8 to the R438 bit endpoint be closed, and can R438 itself rise?", + "why_it_matters": "Past R438 the bit side binds again.", + "first_step": "Exact per-group optimisation instead of greedy; R438 idle-remainder exchanges on its {34:32, 42:320} remainders.", + "blocked_by": "Per-group exact search cost; R438 per-child axis data." + } + ] +} diff --git a/research/rank7-idle-donors-greedy-r438/VERIFY.json b/research/rank7-idle-donors-greedy-r438/VERIFY.json new file mode 100644 index 0000000000..dfd37e163b --- /dev/null +++ b/research/rank7-idle-donors-greedy-r438/VERIFY.json @@ -0,0 +1,21 @@ +{ + "schema_version": 1, + "status": "ready", + "python": "3.12", + "requirements": [], + "inputs": [ + "research/adaptive-kernel-demotion/inputs/DATA-PHASES.json", + "research/r438-native-rehost/CERTIFICATE.json" + ], + "commands": [ + { + "argv": [ + "{python}", + "-B", + "{package}/verify.py" + ], + "timeout_seconds": 300, + "checks": "Independent of build.py: donor axes from own remainder, unhosted receivers, no child both donates and receives, unit/orthogonal-at-receipt and commuting rule, cap 51, profile and rank mass, exact complex root bracket, R438 bit endpoint re-derived (accept at c, reject at c+1e-24), kappa = min(floor24(complex), bit) - 1e-46 - 1e-70 with complex binding, gates over PR3148/PR3184/PR3198; 8 mutation controls rejected." + } + ] +} diff --git a/research/rank7-idle-donors-greedy-r438/build.py b/research/rank7-idle-donors-greedy-r438/build.py new file mode 100644 index 0000000000..5cc5b75574 --- /dev/null +++ b/research/rank7-idle-donors-greedy-r438/build.py @@ -0,0 +1,226 @@ +#!/usr/bin/env python3 +# SPDX-License-Identifier: Apache-2.0 +"""Idle-remainder donor exchanges on PR3148's T740 fill of PR3133's words. + +Every idle remainder of a (replica, port) - including the remainder of a partially hosted bin, +whose axes are the recipe axes [used, cap) - may donate axes to a fully idle (unhosted) child of +the same replica and port. Each moved axis obeys PR1252's commuting rule (commutes with all of the +receiver's current axes, every stage entry/exit X and Y translation, the terminal Y translation and +both children's terminal translations). Receivers are capped at rank 51 (73^2 > 2*51^2). +Phase 1 drains remainders smallest-first into the largest legal receiver; phase 2 runs the +frontier1094 star optimum (PR3184) on the untouched fully idle rank-48 children; phase 3 (new here) +repeats the best single-axis move from a smaller unhosted child to an equal-or-larger unhosted +receiver while it lowers the moment cost. Complex endpoint composed with the R438 bit supplier. + +Inputs (pinned): DATA-PHASES.json on main; PR3148's materialized COMPOSED-FILL/ORDER/DISPATCH and +its PR3133 provider widths (PR3148-PROVIDERS.json, copied from PR3148 vendor/). +""" +import argparse, gzip, hashlib, itertools, json, math +from collections import Counter, defaultdict +from fractions import Fraction as Q +from pathlib import Path + +HERE = Path(__file__).resolve().parent +PHASES = HERE.parents[1] / 'research/adaptive-kernel-demotion/inputs/DATA-PHASES.json' +PIN = dict(phases='c5916ff312678f12aba403847643fbbc29f643acec60bdf836fa56cd3e8251fa', + fill_payload='8f4d6965ba573ff2b71fd7bf6b552643e086739d90bd73c55889502077638e00', + order='927226d702bf3cada076f4c459da9063c0df7e7154a62955cf75c40cf30215b9', + dispatch='90edc935320dd6264e98dc735d868df3c95f5901c70d7d96171001fcb295cce0', + providers='52eb0d85caa7b2d4a93acdf5011f52b793f61ddca86235fb03cd9a09397ad4cd') +T = 740 +LOCAL = {1: 2433, 2: 724, 3: 228, 4: 102, 5: 20, 8: 8} +IDLE_PR3148 = {1: 173160, 3: 48951, 5: 13875, 48: 282569} +BIT = Q('69393850564807966059/40000000000000000000000') # R438 bit endpoint, research/r438-native-rehost CERTIFICATE.json +PR3148_KAPPA = Q('0.0017297774946785970118859999999999999999999998999999999999999999999999') +PR3198_KAPPA = Q('0.0017347705571115131604949999999999999999999998999999999999999999999999') +PR3184_KAPPA = Q('0.0017301890612338507600949999999999999999999998999999999999999999999999') + + +def need(ok, why): + if not ok: raise SystemExit('FAIL: ' + why) + + +def sha(b): return hashlib.sha256(b).hexdigest() +def dot(a, b): return (a & b).bit_count() & 1 +def Hf(r): return 0.0 if r == 0 else r * (73.0 / r) ** 0.00173 + + +def pgz(obj): + d = bytearray(gzip.compress(json.dumps(obj, sort_keys=True, separators=(',', ':')).encode(), mtime=0)); d[9] = 255 + return bytes(d) + + +# ---- exact root (rational intervals, directed rounding 1e-60) ---- +S = 10 ** 60 +def dn(x): return Q(math.floor(x * S), S) +def upr(x): return Q(math.ceil(x * S), S) +def atanh2(z, n): + s, p = Q(0), z + for j in range(n): s += p / (2 * j + 1); p *= z * z + return 2 * s, 2 * p / ((2 * n + 1) * (1 - z * z)) +L2 = atanh2(Q(1, 3), 120) +LN = {} +def lnr(r): + if r not in LN: + x, k = Q(73, r), 0 + while x > 2: x /= 2; k += 1 + a, e = atanh2((x - 1) / (x + 1), 80) + LN[r] = (dn(a + k * L2[0]), upr(a + e + k * (L2[0] + L2[1]))) + return LN[r] +def ex(x0, x1): + def ser(x): + s, t = Q(0), Q(1) + for n in range(1, 40): s += t; t = t * x / n + return s, t + a, _ = ser(x0); b, t = ser(x1) + return dn(a), upr(b + 2 * t) +def moment(prof, b): + W = 896 * T; lo = hi = Q(0) + for r, n in prof.items(): + l0, l1 = lnr(r); e0, e1 = ex(b * l0, b * l1); lo += n * r * e0; hi += n * r * e1 + return lo / (73 * W), hi / (73 * W) +def root(prof, digits=25): + f = lambda b: sum(n * r * (73 / r) ** b for r, n in prof.items()) / (73 * 896 * T) - 1 + a, c = 0.0, 0.01 + for _ in range(200): + m = (a + c) / 2 + if f(m) < 0: a = m + else: c = m + g = 10 ** digits; k0, k1 = int(a * g) - 10 ** 10, int(a * g) + 10 ** 10 + need(moment(prof, Q(k0, g))[1] < 1 and moment(prof, Q(k1, g))[0] > 1, 'bracket') + while k1 - k0 > 1: + k = (k0 + k1) // 2; lo, hi = moment(prof, Q(k, g)) + if hi < 1: k0 = k + elif lo > 1: k1 = k + else: raise SystemExit('wide interval') + return Q(k0, g), Q(k1, g) + + +def main(): + ap = argparse.ArgumentParser(description=__doc__) + ap.add_argument('--t740', type=Path, required=True, help='directory written by PR3148 materialize.py') + a = ap.parse_args() + raw = PHASES.read_bytes(); need(sha(raw) == PIN['phases'], 'phases pin') + rec = {r['port']: r for r in json.loads(raw)['recipes']} + fraw = gzip.decompress((a.t740 / 'COMPOSED-FILL.json.gz').read_bytes()); need(sha(fraw) == PIN['fill_payload'], 'fill pin') + need(sha((a.t740 / 'ORDER.json').read_bytes()) == PIN['order'] and sha((a.t740 / 'DISPATCH.json').read_bytes()) == PIN['dispatch'], 'order/dispatch pins') + praw = (HERE / 'PR3148-PROVIDERS.json').read_bytes(); need(sha(praw) == PIN['providers'], 'providers pin') + prov = json.loads(praw); order = json.loads((a.t740 / 'ORDER.json').read_bytes()) + disp = {(s, r): p for s, r, p in json.loads((a.t740 / 'DISPATCH.json').read_bytes())} + fill = json.loads(fraw) + need(fill['columns'] == ['time', 'helper', 'owner_replica', 'child', 'port', 'offset'] and fill['dispatch_overrides'] == [], 'fill format') + caps = {(p, c): ch['rank'] for p, r in rec.items() for c, ch in enumerate(r['idle_children'])} + AX = {(p, c): [int(v) for v in ch['orthogonal_axes']] for p, r in rec.items() for c, ch in enumerate(r['idle_children'])} + TR = {(p, c): int(ch['translation_after']) for p, r in rec.items() for c, ch in enumerate(r['idle_children'])} + PT = {p: [int(s[k]) for s in rc['stage_alignment'] for k in ('entry_Y', 'exit_Y', 'entry_X', 'exit_X')] + [int(rc['terminal_Y_translation'])] for p, rc in rec.items()} + used, top = Counter(), Counter() + for time, helper, rep, child, port, offset in fill['rows']: + s, r = order[time]; w = prov[disp[s, r]]['widths'][helper] + used[rep, child, port] += w; top[rep, child, port] = max(top[rep, child, port], offset + w) + need(all(used[k] == top[k] for k in used), 'compact helper prefixes') + groups = [] + for rep in range(T): + for p in range(112): + kids = [[c, used[rep, c, p]] for c in range(len(rec[p]['idle_children'])) if caps[p, c] - used[rep, c, p] > 0] + groups.append([rep, p, kids]) + idle = Counter(caps[p, c] - u for _, p, kids in groups for c, u in kids) + need(dict(idle) == IDLE_PR3148, 'idle bill equals PR3148') + + def legal(v, p, c, d, axes_d): + return all(dot(v, x) == 0 for x in axes_d) and all(dot(v, x) == 0 for x in PT[p]) and dot(v, TR[p, c]) == 0 and dot(v, TR[p, d]) == 0 + + def solve(p, kids): + rank = {c: caps[p, c] - u for c, u in kids}; axes = {c: AX[p, c][u:caps[p, c]] for c, u in kids} + hosted = {c: u > 0 for c, u in kids}; role = {c: None for c, _ in kids}; moves = [] + for c in sorted([c for c, u in kids if u > 0], key=lambda c: (rank[c], c)): + for v in list(axes[c]): + best = None + for d in sorted([d for d, _ in kids if not hosted[d] and role[d] != 'D' and d != c and rank[d] < 51], key=lambda d: (-rank[d], d)): + if rank[d] < rank[c] - 1: break + if legal(v, p, c, d, axes[d]): best = d; break + if best is None or Hf(rank[c] - 1) + Hf(rank[best] + 1) - Hf(rank[c]) - Hf(rank[best]) >= 0: continue + axes[c].remove(v); axes[best].append(v); rank[c] -= 1; rank[best] += 1 + role[c] = 'D'; role[best] = 'R'; moves.append([c, best, v]) + free = [c for c, u in kids if u == 0 and role[c] is None and caps[p, c] == 48] + if len(free) >= 2: + MV = {(d, r): [v for v in axes[d] if legal(v, p, d, r, axes[r])] for d in free for r in free if d != r} + best = [len(free) * Hf(48), []] + def match(c, leaves): + opts = [MV[c, l] for l in leaves] + if any(len(o) < 3 for o in opts): return None + def go(k, usedax): + if k == len(leaves): return [] + for trip in itertools.combinations([v for v in opts[k] if v not in usedax], 3): + rest = go(k + 1, usedax | set(trip)) + if rest is not None: return [(c, leaves[k], list(trip))] + rest + return None + return go(0, set()) + def assign(i, roles): + if i == len(free): + leaves = defaultdict(list) + for c in free: + if isinstance(roles[c], tuple): leaves[roles[c][1]].append(c) + cents = [c for c in free if roles[c] == 'c'] + if any(not leaves[c] for c in cents) or any(roles[x] != 'c' for x in leaves): return + mv = [] + for c in cents: + m = match(c, leaves[c]) + if m is None: return + mv += m + rk = [48 - 3 * len(leaves[c]) if roles[c] == 'c' else 51 if isinstance(roles[c], tuple) else 48 for c in free] + cost = sum(Hf(x) for x in rk) + if cost < best[0] - 1e-12: best[0], best[1] = cost, mv + return + c = free[i] + for opt in ['n', 'c'] + [('l', d) for d in free if d != c]: + roles[c] = opt; assign(i + 1, roles) + del roles[c] + assign(0, {}) + for c, l, trip in best[1]: + for v in trip: + axes[c].remove(v); axes[l].append(v); rank[c] -= 1; rank[l] += 1; moves.append([c, l, v]) + un = [c for c, u in kids if u == 0] + while True: + best = None + for c in un: + if role[c] == 'R' or rank[c] == 0: continue + for d in un: + if d == c or role[d] == 'D' or rank[d] >= 51 or rank[d] < rank[c]: continue + g = Hf(rank[c] - 1) + Hf(rank[d] + 1) - Hf(rank[c]) - Hf(rank[d]) + if best is not None and g >= best[0]: continue + for v in axes[c]: + if legal(v, p, c, d, axes[d]): best = (g, c, d, v); break + if best is None or best[0] >= 0: break + g, c, d, v = best + axes[c].remove(v); axes[d].append(v); rank[c] -= 1; rank[d] += 1; role[c] = 'D'; role[d] = 'R'; moves.append([c, d, v]) + return moves, rank + + cache, moves, final = {}, [], Counter() + for rep, p, kids in groups: + key = (p, tuple(map(tuple, kids))) + if key not in cache: cache[key] = solve(p, kids) + mv, rank = cache[key] + moves += [[rep, p] + m for m in mv] + final.update(r for r in rank.values() if r) + prof = Counter({r: n * 9 * T for r, n in LOCAL.items()}); prof.update(final); prof = dict(sorted(prof.items())) + need(sum(r * n for r, n in prof.items()) == 65088 * T and 73 * 73 > 2 * max(prof) ** 2, 'mass and halving') + lo, hi = root(prof) + C = min(Q(math.floor(lo * 10 ** 24), 10 ** 24), BIT) + kappa = C - Q(1, 10 ** 46) - Q(1, 10 ** 70) + need(kappa > PR3198_KAPPA > PR3184_KAPPA > PR3148_KAPPA, 'gates') + (HERE / 'BINS.json.gz').write_bytes(pgz(dict(T=T, columns=['replica', 'port', [['child', 'used']]], groups=[g for g in groups if g[2]]))) + (HERE / 'MOVES.json.gz').write_bytes(pgz(dict(columns=['replica', 'port', 'donor_child', 'receiver_child', 'axis'], moves=moves))) + donors = Counter(); + res = dict(status='PASS_IDLE_DONOR_GREEDY_R438_T740', T=T, axis_moves=len(moves), + donor_children=len({(m[0], m[1], m[2]) for m in moves}), receiver_children=len({(m[0], m[1], m[3]) for m in moves}), + idle_before={str(k): v for k, v in IDLE_PR3148.items()}, idle_after={str(k): v for k, v in sorted(final.items())}, + profile={str(k): v for k, v in prof.items()}, complex_root=[str(lo), str(hi)], + complex_root_decimal=f'{lo.numerator * 10**25 // lo.denominator}e-25', bit=str(BIT), binding='bit' if BIT < lo else 'complex', + kappa=str(kappa), kappa_decimal='0.' + str(kappa.numerator * 10 ** 70 // kappa.denominator).rjust(70, '0'), gain_over_pr3198=str(kappa - PR3198_KAPPA), gain_over_pr3184=str(kappa - PR3184_KAPPA), gain_over_pr3148=str(kappa - PR3148_KAPPA), + max_child_rank=max(prof), halving=[5329, 2 * max(prof) ** 2]) + (HERE / 'RESULT.json').write_text(json.dumps(res, indent=1) + '\n') + print('PASS', float(lo), res['binding'], float(kappa), float(kappa - PR3184_KAPPA), len(moves)) + + +if __name__ == '__main__': + main() diff --git a/research/rank7-idle-donors-greedy-r438/verify.py b/research/rank7-idle-donors-greedy-r438/verify.py new file mode 100644 index 0000000000..4083be130e --- /dev/null +++ b/research/rank7-idle-donors-greedy-r438/verify.py @@ -0,0 +1,219 @@ +#!/usr/bin/env python3 +# SPDX-License-Identifier: Apache-2.0 +"""Independent verifier (does not import build.py) for the idle-remainder donor exchanges. + +Re-derives from BINS / MOVES / DATA-PHASES: donor axes come from the donor's own idle remainder +(recipe axes [used, cap)); receivers are unhosted (used == 0); no child both donates and receives; +every moved axis is a unit vector orthogonal to all of the receiver's axes held at that moment and +commutes with every stage entry/exit X/Y translation, the terminal Y translation and both +children's terminal translations; final ranks <= 51; per-group axis multisets unchanged; the +complete profile and rank mass; an exact complex root bracket with its own interval arithmetic; +kappa = min(floor24(complex_lower), PR589 bit) - 1e-46 - 1e-70 and its gates. +Optional --t740 rebinds BINS to PR3148's materialized fill. Mutation controls must be rejected. +""" +import argparse, copy, gzip, hashlib, json +from collections import Counter, defaultdict +from fractions import Fraction as F +from pathlib import Path + +PKG = Path(__file__).resolve().parent +PHASES = PKG.parents[1] / 'research/adaptive-kernel-demotion/inputs/DATA-PHASES.json' +T = 740 +LOCAL = {1: 2433, 2: 724, 3: 228, 4: 102, 5: 20, 8: 8} +IDLE = {1: 173160, 3: 48951, 5: 13875, 48: 282569} +BITCERT = PKG.parents[1] / 'research/r438-native-rehost/CERTIFICATE.json' +BIT = None # R438 bit endpoint, re-derived from its certificate's bit profile in check_bit() +GATES = dict(PR3198=F('0.0017347705571115131604949999999999999999999998999999999999999999999999'), PR3148=F('0.0017297774946785970118859999999999999999999998999999999999999999999999'), + PR3184=F('0.0017301890612338507600949999999999999999999998999999999999999999999999')) + + +class Reject(Exception): pass +def req(ok, why): + if not ok: raise Reject(why) +def load(p): + b = Path(p).read_bytes(); return json.loads(gzip.decompress(b) if b[:2] == b'\x1f\x8b' else b) +def par(a, b): return bin(a & b).count('1') & 1 + + +def audit(rec, bins, moves): + caps = {(p, c): ch['rank'] for p, r in rec.items() for c, ch in enumerate(r['idle_children'])} + G = {} + for rep, p, kids in bins['groups']: + req((rep, p) not in G and 0 <= rep < T and p in rec, 'group key') + G[rep, p] = {c: u for c, u in kids} + req(all(0 <= u < caps[p, c] for c, u in kids), 'used below capacity') + req(Counter(caps[p, c] - u for (rep, p), kids in G.items() for c, u in kids.items()) == Counter(IDLE), 'idle bill') + trans = {} + for p, rc in rec.items(): + trans[p] = {int(s[k]) for s in rc['stage_alignment'] for k in ('entry_X', 'exit_X', 'entry_Y', 'exit_Y')} | {int(rc['terminal_Y_translation'])} + for c, ch in enumerate(rc['idle_children']): + ax = [int(v) for v in ch['orthogonal_axes']] + req(all(par(v, v) == 1 for v in ax) and all(par(a, b) == 0 for i, a in enumerate(ax) for b in ax[i + 1:]), 'recipe axes orthonormal') + state = {} + def cur(rep, p, c): + k = (rep, p, c) + if k not in state: + u = G[rep, p][c]; state[k] = dict(axes=set(int(v) for v in rec[p]['idle_children'][c]['orthogonal_axes'][u:caps[p, c]]), role=None) + return state[k] + for m in moves: + rep, p, c, d, v = m + req((rep, p) in G and c in G[rep, p] and d in G[rep, p] and c != d, 'children of the group') + req(G[rep, p][d] == 0, 'receiver must be unhosted') + sc, sd = cur(rep, p, c), cur(rep, p, d) + req(sc['role'] != 'R' and sd['role'] != 'D', 'child both donates and receives') + own = set(int(x) for x in rec[p]['idle_children'][c]['orthogonal_axes'][G[rep, p][c]:caps[p, c]]) + req(v in sc['axes'] and v in own, 'axis not in donor remainder') + req(par(v, v) == 1 and all(par(v, x) == 0 for x in sd['axes']), 'axis not orthogonal to receiver axes') + tc = int(rec[p]['idle_children'][c]['translation_after']); td = int(rec[p]['idle_children'][d]['translation_after']) + req(all(par(v, x) == 0 for x in trans[p] | {tc, td}), 'axis does not commute with translations') + sc['axes'].discard(v); sd['axes'].add(v); sc['role'] = 'D'; sd['role'] = 'R' + req(len(sd['axes']) <= 51, 'rank above 51') + final = Counter() + for (rep, p), kids in G.items(): + for c, u in kids.items(): + r = len(state[rep, p, c]['axes']) if (rep, p, c) in state else caps[p, c] - u + if r: final[r] += 1 + return final + + +def mom(prof, b): + Q72 = 10 ** 72 + def rd(x): return F(x.numerator * Q72 // x.denominator, Q72) + def ru(x): return F(-((-x.numerator * Q72) // x.denominator), Q72) + def at(z, n): + s, p = F(0), z + for j in range(n): s += p / (2 * j + 1); p *= z * z + return 2 * s, 2 * p / ((2 * n + 1) * (1 - z * z)) + l2 = at(F(1, 3), 130); W = 896 * T; lo = hi = F(0) + for r, n in sorted(prof.items()): + y, k = F(73, r), 0 + while y >= 2: y /= 2; k += 1 + a, e = at((y - 1) / (y + 1), 90) + L0, L1 = rd(a + k * l2[0]), ru(a + e + k * (l2[0] + l2[1])) + def tay(x): + s, t = F(1), F(1) + for j in range(1, 34): t = t * x / j; s += t + return s, t * x / 34 * 3 + e0, _ = tay(b * L0); e1, t1 = tay(b * L1) + lo += n * r * rd(e0); hi += n * r * ru(e1 + t1) + return lo / (73 * W), hi / (73 * W) + + +def check_bit(): + inv = json.loads(BITCERT.read_text())['pipeline']['candidate']['hosted']['invoice'] + prof = {int(k): v for k, v in inv['bit_profile'].items()} + c, cn = F(inv['bit_lower']), F(inv['next_grid_point_rejected']) + req(c == F(inv['bit_lower_decimal']) and cn - c == F(1, 10 ** 24) and 2 * max(prof) ** 2 < 64 ** 2, 'R438 certificate fields') + W = 28416; N = sum(prof.values()) + def bm(b): + lo = hi = F(0) + for r, n in sorted(prof.items()) + [(1, F(32 * 64 * 64 * N, 10 ** 16))]: + l0, l1 = ln64(r); e0, e1 = exbox(b * l0, b * l1); lo += n * r * e0; hi += n * r * e1 + return lo / (64 * W), hi / (64 * W) + req(bm(c)[1] < 1 and bm(cn)[0] > 1, 'R438 bit endpoint accepted at c, rejected at c+1e-24') + return c + + +def ln64(r): + Q72 = 10 ** 72 + def at(z, n): + s, p = F(0), z + for j in range(n): s += p / (2 * j + 1); p *= z * z + return 2 * s, 2 * p / ((2 * n + 1) * (1 - z * z)) + y, k = F(64, r), 0 + while y >= 2: y /= 2; k += 1 + l2 = at(F(1, 3), 130); a, e = at((y - 1) / (y + 1), 90) + return F((a + k * l2[0]).numerator * Q72 // (a + k * l2[0]).denominator, Q72), F(-((-(a + e + k * (l2[0] + l2[1])).numerator * Q72) // (a + e + k * (l2[0] + l2[1])).denominator), Q72) + + +def exbox(x0, x1): + def tay(x): + s, t = F(1), F(1) + for j in range(1, 34): t = t * x / j; s += t + return s, t * x / 34 * 3 + a, _ = tay(x0); b, t = tay(x1) + return a, b + t + + +def run(rec, bins, moves, result): + final = audit(rec, bins, moves) + prof = Counter({r: n * 9 * T for r, n in LOCAL.items()}); prof.update(final); prof = dict(sorted(prof.items())) + req({str(k): v for k, v in prof.items()} == result['profile'], 'declared profile') + req(sum(r * n for r, n in prof.items()) == 65088 * T, 'rank mass 65088*T') + req(max(prof) <= 51 and 73 * 73 > 2 * max(prof) ** 2, 'halving guard') + lo, hi = F(result['complex_root'][0]), F(result['complex_root'][1]) + req(hi - lo == F(1, 10 ** 25) and mom(prof, lo)[1] < 1 and mom(prof, hi)[0] > 1, 'complex root bracket') + C = min(F(lo.numerator * 10 ** 24 // lo.denominator, 10 ** 24), BIT) + req(C < BIT, 'complex binds below the R438 bit endpoint') + kappa = C - F(1, 10 ** 46) - F(1, 10 ** 70) + req(kappa == F(result['kappa']), 'headline kappa') + for n, g in GATES.items(): req(kappa > g, 'kappa must exceed ' + n) + return prof, kappa, lo + + +def main(): + ap = argparse.ArgumentParser(description=__doc__) + ap.add_argument('--t740', type=Path) + ap.add_argument('--providers', type=Path, default=PKG / 'PR3148-PROVIDERS.json') + ap.add_argument('--write', action='store_true', help='rewrite the committed AUDIT.json receipt') + a = ap.parse_args() + if not __debug__: raise SystemExit('assertions required') + raw = PHASES.read_bytes() + req(hashlib.sha256(raw).hexdigest() == 'c5916ff312678f12aba403847643fbbc29f643acec60bdf836fa56cd3e8251fa', 'phases pin') + rec = {r['port']: r for r in json.loads(raw)['recipes']} + global BIT + BIT = check_bit() + bins, mv, result = load(PKG / 'BINS.json.gz'), load(PKG / 'MOVES.json.gz')['moves'], load(PKG / 'RESULT.json') + rebound = False + if a.t740: + fraw = gzip.decompress((a.t740 / 'COMPOSED-FILL.json.gz').read_bytes()) + req(hashlib.sha256(fraw).hexdigest() == '8f4d6965ba573ff2b71fd7bf6b552643e086739d90bd73c55889502077638e00', 'fill pin') + prov = load(a.providers); order = load(a.t740 / 'ORDER.json'); disp = {(s, r): p for s, r, p in load(a.t740 / 'DISPATCH.json')} + used = Counter() + for time, helper, rep, child, port, offset in json.loads(fraw)['rows']: + s, r = order[time]; used[rep, child, port] += prov[disp[s, r]]['widths'][helper] + caps = {(p, c): ch['rank'] for p, r in rec.items() for c, ch in enumerate(r['idle_children'])} + derived = [[rep, p, [[c, used[rep, c, p]] for c in range(len(rec[p]['idle_children'])) if caps[p, c] - used[rep, c, p] > 0]] for rep in range(T) for p in range(112)] + req([g for g in derived if g[2]] == bins['groups'], 'BINS equal the fill') + rebound = True + prof, kappa, lo = run(rec, bins, mv, result) + rej = {} + first_hosted = next(i for i, m in enumerate(mv) if {c: u for c, u in next(g for g in bins['groups'] if g[0] == m[0] and g[1] == m[1])[2]}[m[2]] > 0) + rep, p, c, d, v = mv[first_hosted] + kids = {cc: u for cc, u in next(g for g in bins['groups'] if g[0] == rep and g[1] == p)[2]} + hosted_other = next((cc for cc, u in kids.items() if u > 0 and cc != c), None) + used_axis = int(rec[p]['idle_children'][c]['orthogonal_axes'][0]) + def mut(f): + x = copy.deepcopy(mv); f(x); return x + cases = dict( + hosted_receiver=mut(lambda x: x.__setitem__(first_hosted, [rep, p, c, hosted_other if hosted_other is not None else c, v])), + hosted_axis_from_used_prefix=mut(lambda x: x.__setitem__(first_hosted, [rep, p, c, d, used_axis])), + foreign_axis=mut(lambda x: x.__setitem__(first_hosted, [rep, p, c, d, 1 << 80])), + axis_moved_twice=mut(lambda x: x.insert(first_hosted + 1, list(x[first_hosted]))), + receiver_donates=mut(lambda x: x.append([rep, p, d, c, v])), + dropped_move=mut(lambda x: x.pop(first_hosted)), + ) + for name, x in cases.items(): + try: run(rec, bins, x, result) + except Reject as e: rej[name] = str(e) + else: raise SystemExit('mutation accepted: ' + name) + r2 = copy.deepcopy(result); r2['complex_root'] = [str(lo + F(1, 10 ** 25)), str(lo + F(2, 10 ** 25))] + try: run(rec, bins, mv, r2) + except Reject as e: rej['next_root_grid'] = str(e) + else: raise SystemExit('mutation accepted: next_root_grid') + r3 = copy.deepcopy(result); r3['kappa'] = str(F(result['kappa']) + F(1, 10 ** 24)) + try: run(rec, bins, mv, r3) + except Reject as e: rej['kappa_above_bit'] = str(e) + else: raise SystemExit('mutation accepted: kappa_above_bit') + out = dict(status='PASS_IDLE_DONOR_GREEDY_R438_AUDIT', moves=len(mv), fill_rebound=rebound, kappa=str(kappa), + complex_root_lower=str(lo), binding='bit' if BIT < lo else 'complex', rejected_controls=rej) + if a.write: (PKG / 'AUDIT.json').write_text(json.dumps(out, indent=1, sort_keys=True) + '\n') + else: + strip = lambda d: {k: v for k, v in d.items() if k != 'fill_rebound'} + req(strip(load(PKG / 'AUDIT.json')) == strip(json.loads(json.dumps(out))), 'committed AUDIT.json receipt') + print('PASS_IDLE_DONOR_GREEDY_R438_AUDIT moves=%d controls=%d kappa=%s binding=%s' % (len(mv), len(rej), float(kappa), out['binding'])) + + +if __name__ == '__main__': + try: main() + except Reject as e: raise SystemExit('FAIL: ' + str(e))

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