Skip to content

Execute R437 nonzero-high leaf payload on two complete fibers #4793

New issue

Have a question about this project? Sign up for a free GitHub account to open an issue and contact its maintainers and the community.

Sign up for GitHub

By clicking “Sign up for GitHub”, you agree to our terms of service and privacy statement. We’ll occasionally send you account related emails.

Already on GitHub? Sign in to your account

Merged
Mister-Meeseeks merged 1 commit into from
Oct 23, 2026
Merged

Execute R437 nonzero-high leaf payload on two complete fibers #4793

Show file tree
Hide file tree
Changes from all commits
Commits
Show all changes
1 commit
Select commit
File filter

Filter by extension

Filter by extension
Conversations
Failed to load comments.
Loading
Jump to
Jump to file
Failed to load files.
Loading
Diff view
Diff view
123 changes: 123 additions & 0 deletions research/r437-nonzero-high-leaf/README.md
View file
Open in desktop
Original file line number Diff line number Diff line change
@@ -0,0 +1,123 @@
# Nonzero-high R437 leaf payload on two complete fibers

This is a finite physical payload certificate at **q=3, w=2**, using the actual
R437 D compiler request 1676 (SOURCE87), actual `SelectedBinding.child_program`,
actual incoming coefficient evaluator, actual `trace.leaf`/`packet_engine.run`,
and the literal next SOURCE87 XOR consumer. It executes 13,122 dirty bits in two
complete 6,561-bit four-atom fibers. The two nonzero high matrices produce
coordinate weights `[8,2]` and `[5,8]` modulo 9. All 24 split/merge coefficient
preparations execute; none is replaced by a metadata observer.

**This does not execute the full high cube or prove original-root reachability.**
The source-valid borrowed Program is rooted at width 2048/unit 2 with a GOOD
2048→64 history step. The actual constructor appends 64→2. Both represented
prefixes produce byte-identical child Programs. The fixture is historical R437
semantics; q=3 is not admitted by the currently selected numerical root domain.
The physical trace is a four-atom leaf called directly, not a full `Machine.node`
or a claimed execution of the production parent GL64 gather and residual.

## Increment and predecessor credit

Chris R / Clear1nsight's #4176 (`r437-carrier-integration/PHYSICAL.md`) already
executes a produced two-step child, twelve callbacks, dirty payload and SOURCE87
consumer at q=3,w=1, including external spectators. That is credited, not claimed
again. The new boundary is nonzero encoded high matrices and genuine modulus-9
weights, where inversion differs from identity. #4759 (`r437-leaf-dispatch`,
ff9c82bcaf19b57edfbea69f92675626cd4c8fca) establishes root-produced ingress and
Machine.block chronology with a metadata observer; this package does **not**
compose its independent ancestry fixture into the present borrowed history.
#4757 (5dba1acc2ef67e65e6a40e963f727b01edc5e132) is the distinct q127 parameter
entry/stock-only adapter and supplies no physical execution claim here.

The caller, binary arithmetic, compiler and source families are the upstream
contributors' unchanged implementations. `SOURCES.json` binds 401 live input
files at canonical base 624de9dc66858af0945e5f8a0942488d62280d43. The package-local
historical selected record is authenticated by SHA256; its isolated projection
is used only by the unchanged historical loader. The selected frontier is not
edited. The new harness and derivation are by Brian (JoyboyBrian), with substantial
OpenAI Codex assistance, Apache-2.0.

## Chart and independent output derivation

Let P be the exact source preparation modulo 9. For active index i=0,1 and
inactive j=i+2, use the invertible 2×2 header block `[[1,1],[p_i−1,p_i]]`, determinant
one. Elsewhere use the identity. Set chart=header·P⁻¹. All chosen p_i are 2 modulo
3, so these charts share one actual compiler-resolved GOOD low class. Their
canonical high digits `(chart−low)/3` lie in {0,1,2} and are nonzero. The independent
oracle constructs the rank-two projector header[:,0:2]·header⁻¹[0:2,:] and checks
its actual leading pivots. A diagonal scaling alone would leave this projector
unchanged, so it would not be a discriminating high-field fixture.

Ancestor pivots are [2,5]. For child coordinates 0 and 1 the ancestor's
floor(2048/64)=32 gives pivot0. Root unit2 therefore contributes 4, while the
current 64→2 step contributes p_i. Current pivots [2,5] and [8,2] yield [8,2]
and [5,8]. The three ADDs request λ, −λ⁻¹, λ, each once per split and merge.
Runtime `Word.inspect` is disabled; the observer saves the original method to
compare outputs and never returns decoded data to the algorithm.

For one paired coordinate, the literal eight primitives have pullback matrix
`S A(λ) S A(−λ⁻¹) S A(λ) S D = [[0,λ],[λ⁻¹,0]]`, where
`A(c)=[[1,0],[−c,1]]` and `D=diag(1,−1)`. For coordinates `(x0,x1,y0,y1)` the
independent permutation is `(λ0*y1, λ1*y0, λ1⁻¹*x1, λ0⁻¹*x0) mod9`.
The verifier enumerates all 9⁴ coordinates per fiber, checks bijectivity, and
compares every output bit. Reusing prefix0 weights for prefix1 and exchanging
weights with their inverses both change the dirty expected output.

## Exact finite restriction and intertwining

The production `directory.Odometer.advance` increments the last matrix entry
first. Thus `n(H)=Σ H[k]3^(4095−k)` is the high index. The verifier constructs and
decodes the two distinct indices and checks every local coordinate's global
offset `E_i(j)=n(H_i)*9⁴+j` within this fixed old-prefix and low-class
block. This is a global high-cube offset for that block, not an asserted offset
through all old prefixes, low classes or full-parent spectator coordinates. It checks `floor(E_i(j)/9⁴)=n(H_i)` and
`E_i(j)%9⁴=j`, and that the independent permutation stays in that same fiber.

This indexing alone is not the separability argument. In authenticated
`packet_engine.run_generator`, each primitive resets an output tape, loops over
complete prefixes, calls `read_prefix`, copies exactly one `shape.fibre`, executes
the primitive on that local tape, and appends its return. No primitive reads a
neighboring prefix's payload. Coefficients read the current complete prefix plus
the same borrowed Program. `episode.xor_packet` loops old prefixes, then
`context.highs`, then exactly `fibre` bits and performs pointwise XOR. Therefore
for each fixed full prefix, projection π_i commutes with each primitive and the
XOR consumer; induction over the finite trace gives π_i T = T_i π_i. Embedding
commutes on the selected support, with all other fibers left to their own T_j.
No claim is made that full T is identity on omitted fibers.

The explicit adapter sets prefix count and the consumer's `context.highs` to 2,
and supplies precisely those two complete prefixes in matching payload order.
It replaces infeasible independent copies only. It does not replace a numeric
primitive or callback. Full `3^4096` enumeration, full parent spectator expansion,
GL64 gather and physical field generation are unexecuted. The two represented
prefixes have different dirty data and weights; source and target bytes/heads
must remain unchanged. This is not an inference from one repeated fiber.

## Checks and invoice

The actual callback rejects high digit3 and a produced STEP changed from rank2
to rank3, restoring borrowed bytes/heads and numerical ownership. A one-bit wrong
child return changes the result of the actual XOR consumer. Positive execution
checks all 24 callback events, fresh owned output, the full oracle comparison,
consumer event `[1,467,87,1,509,0]` at position22398, preserved borrowed inputs,
and erased backing for every newly allocated record tape. The two-prefix
Program construction, controls, child trace, consumer and cleanup are included
in the separate record/index/residue action receipt. Host fixture/oracle/source
compilation and initial borrowed construction are outside that runtime invoice.
No uniform tariff, improvement in κ, complete multiplication theorem or supplier
admission follows from this invoice.

Run `python3.12 -I -B research/r437-nonzero-high-leaf/verify.py` (also with `-O`).
`VERIFY.json` registers both deterministic replays. `RESULT.json` is compared
with JSON typed equality, including boolean/integer distinctions. This is an
author-checked finite certificate plus a scoped source argument, not formal
kernel verification or a hosted-CI claim.

## Open next questions

1. Join an admitted original-root produced history to a nonzero-high physical
child and explicit GL64 gather without conflating the independent fixtures.
2. Implement the full high directory/fiber generation or a physically charged
symbolic representation; the two-prefix restriction is not that implementation.
3. Pay the full production spectators, gather, residual and precision/stock
obligations before drawing a uniform supplier conclusion.
235 changes: 235 additions & 0 deletions research/r437-nonzero-high-leaf/RESULT.json
View file
Open in desktop
Original file line number Diff line number Diff line change
@@ -0,0 +1,235 @@
{
"borrowed_preserved": true,
"callback_calls": [
{
"coordinate": 0,
"negative_inverse": false,
"prefix": 0,
"value": 8
},
{
"coordinate": 0,
"negative_inverse": false,
"prefix": 0,
"value": 8
},
{
"coordinate": 0,
"negative_inverse": false,
"prefix": 1,
"value": 5
},
{
"coordinate": 0,
"negative_inverse": false,
"prefix": 1,
"value": 5
},
{
"coordinate": 0,
"negative_inverse": true,
"prefix": 0,
"value": 1
},
{
"coordinate": 0,
"negative_inverse": true,
"prefix": 0,
"value": 1
},
{
"coordinate": 0,
"negative_inverse": true,
"prefix": 1,
"value": 7
},
{
"coordinate": 0,
"negative_inverse": true,
"prefix": 1,
"value": 7
},
{
"coordinate": 0,
"negative_inverse": false,
"prefix": 0,
"value": 8
},
{
"coordinate": 0,
"negative_inverse": false,
"prefix": 0,
"value": 8
},
{
"coordinate": 0,
"negative_inverse": false,
"prefix": 1,
"value": 5
},
{
"coordinate": 0,
"negative_inverse": false,
"prefix": 1,
"value": 5
},
{
"coordinate": 1,
"negative_inverse": false,
"prefix": 0,
"value": 2
},
{
"coordinate": 1,
"negative_inverse": false,
"prefix": 0,
"value": 2
},
{
"coordinate": 1,
"negative_inverse": false,
"prefix": 1,
"value": 8
},
{
"coordinate": 1,
"negative_inverse": false,
"prefix": 1,
"value": 8
},
{
"coordinate": 1,
"negative_inverse": true,
"prefix": 0,
"value": 4
},
{
"coordinate": 1,
"negative_inverse": true,
"prefix": 0,
"value": 4
},
{
"coordinate": 1,
"negative_inverse": true,
"prefix": 1,
"value": 1
},
{
"coordinate": 1,
"negative_inverse": true,
"prefix": 1,
"value": 1
},
{
"coordinate": 1,
"negative_inverse": false,
"prefix": 0,
"value": 2
},
{
"coordinate": 1,
"negative_inverse": false,
"prefix": 0,
"value": 2
},
{
"coordinate": 1,
"negative_inverse": false,
"prefix": 1,
"value": 8
},
{
"coordinate": 1,
"negative_inverse": false,
"prefix": 1,
"value": 8
}
],
"child_width": 2,
"complete_fiber_bits": 6561,
"consumer_sha256": "0f8e16924fd79d5c002ecafd4b77ac929a97f186b71c9fcf64992c6490a126f2",
"controls": [
"canonical high digit",
"actual selected rank",
"one-bit wrong return changes actual SOURCE87 consumer",
"stale prefix0 coefficient vector changes second fiber",
"inverse-weight substitution changes actual output"
],
"full_high_cube_count": {
"bits": 6493,
"sha256": "4acde110321e89dc1be1c4b81709f91e8298a1bbff8c80d0d86adaf5b112eac2"
},
"full_high_cube_executed": false,
"global_fiber_offsets": [
{
"bits": 6498,
"sha256": "b2b36d04fd96500a40dd12c2b324767cf611604882bbe53fec169e03944e8c3e"
},
{
"bits": 6498,
"sha256": "c8c7ca64fcdbf9a736c359099b045ee3d1ea7ee011730d26b07dc6f278ac66a6"
}
],
"global_high_indices": [
{
"bits": 6486,
"sha256": "d5e0075b1dac0a9498d27ef42281f4e9905c83ce6c8a4eba3475b374fd70561c"
},
{
"bits": 6486,
"sha256": "7238e2dfd72a89b6e6e34610046f5adfa6ad25fb3cd65d6575ee3862583c6c85"
}
],
"invoice": {
"index": {
"moves": 898628,
"reads": 916003,
"writes": 189312
},
"record": {
"moves": 45836400,
"reads": 52988394,
"writes": 10776087
},
"residue": {
"moves": 177295714,
"reads": 169719848,
"writes": 34956265
}
},
"literal_consumer_event": [
1,
467,
87,
1,
509,
0
],
"literal_consumer_position": 22398,
"live_inputs": 401,
"modulus": 9,
"numerical_admitted": false,
"owned_erased": true,
"produced_program_sha256": "a8293367597b7cb38efad9fd7b23224425b7d515b8088bf0302f225246a75ab0",
"q": 3,
"return_sha256": "4190faad3418b114a03f8116aaf352aafd2717109fef13827483f6c12306bc50",
"root_width": 2048,
"scope": "Actual leaf and XOR payload on two selected high-prefix fibers; full high cube, original-root reachability/admission, GL64 producer and uniform tariff unexecuted.",
"selected_prefix_count": 2,
"source_identity": "d854ee52df07cce2a47ded48539f6c25266c0c6f245c7b10a5dcafbb03f71a3b",
"source_request": 1676,
"status": "PASS_R437_NONZERO_HIGH_LEAF",
"total_executed_bits": 13122,
"w": 2,
"weights": [
[
8,
2
],
[
5,
8
]
]
}
Loading