Independent transfer audit (no new κ): PR4091's pooled ceiling applies to the retained PR4088 head; remaining headroom 1.140318244487202e-9

research/fourth-entry-ceiling-transfer/README.md

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+# Does PR4091's pooled ceiling transfer to the retained PR4088 head?
+
+Independent source-bound transfer audit, priority revision 7 card
+`independent-moment`. **No new kappa, no supplier admission, and no change to
+the selected record.**
+
+PR4091 (`research/staged-fourth-mixture-ceiling`) certifies a sharp pooled
+ceiling `0.001730980255989036959962..963` for a fixed two-provider invoice
+pinned to PR4088 head `76088d49e3ed4142a958659aa996b0ca4da5e88e`
+(1,080 fourth-entry calls of 3,240). The retained PR4088 head on main
+(`research/staged544-mixed-fourth-entry`, `72d7efc181edb21806a878f174847c96
+dd410ab0`) uses 1,090 fourth-entry calls. Revision 7 requires verifying word,
+capacity and stock equivalence before applying the ceiling to the later fill.
+
+## Verdict (all checks pass; `verify.py`)
+
+1. **Words identical byte-for-byte.** All four shared scalar-word inputs
+   (`THREE/FOUR × base/extra`) hash identically (gzip payload and canonical
+   JSON) between the ceiling package's `source4088/inputs/` freeze and the
+   retained head's `inputs/`: 4/4. The four-entry profile derived from
+   PR4091's published `L3` and `d = L4-L3` equals PR4088's published table.
+2. **Capacity and stock identical.** Bin inventory `8:241,920`,
+   `16/32/48: 161,280` each, total 725,760 bins (= 360 replicas × 2,016),
+   agrees with the later fill's published totals (725,760 bins; 1,321,920
+   roles); the residual mass is constant at 162,900 across both fills.
+3. **Same word law.** Each package's published paid profile decomposes
+   uniquely as `3,240 x L3 + x (L4-L3) + idle residuals`, with `x` derived
+   independently from rank-1, rank-3 and rank-4 coordinates giving exactly
+   the published fourth-call counts (1,080 and 1,090).
+4. **Independent moment reproduction.** A fresh Decimal bisection of
+   `sum_r n_r (r/73)^(1-a) / (896*360) = 1` (no reuse of either package's
+   solver) reproduces all three published roots inside their own brackets:
+   pooled optimum `0.001730980255989036959962261...` (the ceiling), pinned
+   literal `0.001730978305075885693430489...`, and the later head
+   `0.001730979115670792472760579...`.
+5. **Transfer verdict with exact numbers.** The later root stays strictly
+   below the ceiling; remaining headroom is
+   `1.140318244487202e-9`, i.e. 58.45% of the original
+   `1.950913151266532e-9` margin. The consumed `8.10594906779330e-10`
+   agrees with PR4088's published gain over its previous revision
+   (`>= 8.10594906779328e-10`, checked as exact rationals).
+
+## Reproduction
+
+From the repository root with standard-library Python 3.12:
+
+```sh
+python3.12 -B scripts/research_package.py --package research/fourth-entry-ceiling-transfer
+python3.12 -B scripts/check_research_commit.py --package research/fourth-entry-ceiling-transfer --check-source-history
+python3.12 -I -Werror -B research/fourth-entry-ceiling-transfer/verify.py
+python3.12 -I -O -Werror -B research/fourth-entry-ceiling-transfer/verify.py
+python3.12 -I -Werror -B research/fourth-entry-ceiling-transfer/test_verify.py
+```
+
+`verify.py` reads only the two retained packages and the selected record;
+`test_verify.py` carries five rejecting controls (extra rank-1 children,
+wrong stock divisor, tampered word delta, corrupted word payload, shifted
+idle total). `RESULT.json` is the generated evidence snapshot.
+
+## Scope and limits
+
+This is a finite source-bound audit of two retained packages: premise
+equivalence plus independent recomputation of their published moment roots.
+Not re-derived here:
+
+- PR4091's 841 whole-helper-pattern coverage and its three dual certificates
+  are taken as published; this audit does not replay that coverage proof.
+- Whether legal exchanges can reach an arbitrary idle multiset with the same
+  residual total (PR4091's own open question) remains open; the transfer
+  verdict is at the level of the pooled model's premises, not chronological
+  attainability.
+- Native, owner/phase, chronology, precision, tape, BIT and outer-transfer
+  obligations are inherited unchanged; the selected #1094 record and its
+  kappa `0.001672660197076918` are untouched.
+
+## Open next questions
+
+- Can a legal chronological exchange reach the pooled eight-pattern idle
+  multiset at x=1090 (PR4091 open question 1, now with the exact remaining
+  headroom `1.140318244487202e-9` stated against the retained head)?
+- Do later PR4088 revisions that change any word, capacity or stock premise
+  invalidate the transfer for subsequent ceilings? Any such change requires a
+  new model per PR4091's own scope note.
+
+Prepared by Nick Petalas with AI assistance. Credit Ross Richardson/PR4091
+and Cinna Davis/PR4088 with their packages' full retained lineages
+(Rohan Arun/PR4076, Dugongue and David Ganz/PR4085/3945, dataisfire/PR3734,
+ChaloupeMusic and Erwan Secousses/PR3949/3815, and the staged-release,
+solver, native, owner and transfer lineage). Apache-2.0.

research/fourth-entry-ceiling-transfer/RESULT.json

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+{
+  "assumptions_not_rederived": [
+    "PR4091's 841 whole-helper pattern coverage and three dual certificates are not replayed here; the ceiling is taken as published by its own package.",
+    "Whether every literal exchange may reach an arbitrary idle multiset with the same residual total (PR4091 open question 1) is not settled by this audit.",
+    "Native, owner/phase, chronology, precision, tape, BIT and outer transfer obligations are inherited from the pinned packages and are not re-verified."
+  ],
+  "bill": {
+    "W": 322560,
+    "form": "sum_r n_r (r/m)^(1-a) / W",
+    "m": 73
+  },
+  "bin_inventory": {
+    "ceil_bin_counts_match": true,
+    "ceil_bin_total": true,
+    "ceil_bins_divide_replicas": true,
+    "idle_total_ceiling": 162900,
+    "idle_total_constant": true,
+    "idle_total_mixed": 162900,
+    "mix_publishes_bin_total": true,
+    "mix_publishes_role_total": true
+  },
+  "card": "independent-moment",
+  "ceiling_bracket": [
+    "0.001730980255989036959962",
+    "0.001730980255989036959963"
+  ],
+  "moments": {
+    "ceil_minus_later_upper_decimal": "1.140318244487202000000000000000e-9",
+    "ceiling_profile_root_reproduced": true,
+    "later_root_below_ceiling": true,
+    "later_root_in_own_bracket": true,
+    "margin_consumed_decimal": "8.105949067793300000000000000000e-10",
+    "margin_consumed_ge_published_gain": true,
+    "pinned_headroom_decimal": "1.950913151266532000000000000000e-9",
+    "pinned_literal_profile_parsed_from_proof": true,
+    "pinned_literal_root_reproduced": true,
+    "pinned_root_matches_later_packages_pin": true,
+    "remaining_over_original_float": 0.5845048733957777,
+    "remaining_over_original_ratio": "383679195/656417444",
+    "root_later_head": "0.00173097911567079247276057992930279289376037876463631692371950",
+    "root_pinned_literal": "0.00173097830507588569343048924930444139646206355277330146761050",
+    "root_pooled_optimum": "0.00173098025598903695996226153870190172368895322140797406630050"
+  },
+  "pinned_head_pr4088": "76088d49e3ed4142a958659aa996b0ca4da5e88e",
+  "question": "Does PR4091's fixed-inventory pooled ceiling transfer to the retained later PR4088 head?",
+  "retained_head_pr4088": "72d7efc181edb21806a878f174847c96dd410ab0",
+  "schema_version": 1,
+  "status": "TRANSFER_SUPPORTED_AT_MODEL_PREMISES",
+  "word_file_payload_equal": 4,
+  "word_files": [
+    {
+      "canonical_equal": true,
+      "container_sha256_new": "df31495cff95a1e512da398f52841c6b5ade29067869b3d68b89d756a5641112",
+      "container_sha256_old": "df31495cff95a1e512da398f52841c6b5ade29067869b3d68b89d756a5641112",
+      "file": "THREE-base.json.gz",
+      "payload_equal": true,
+      "payload_sha256": "960867f94fe43489c5108eaff4cc159714a338a8a056837e5c497ded3d72c283",
+      "present": true
+    },
+    {
+      "canonical_equal": true,
+      "container_sha256_new": "9a28f7ef91938c0866e408eb06e03eb5f8e727a00b44eb936ddd5ed48704bd4c",
+      "container_sha256_old": "9a28f7ef91938c0866e408eb06e03eb5f8e727a00b44eb936ddd5ed48704bd4c",
+      "file": "THREE-extra.json.gz",
+      "payload_equal": true,
+      "payload_sha256": "ef1ca8b7d40346fc2b3261b93dab740322064e47ea194b7d989bac3650e37255",
+      "present": true
+    },
+    {
+      "canonical_equal": true,
+      "container_sha256_new": "aecaddba48fdff6353a6511c3623346b05aa607e30103fb016604a2b1025ce95",
+      "container_sha256_old": "aecaddba48fdff6353a6511c3623346b05aa607e30103fb016604a2b1025ce95",
+      "file": "FOUR-base.json.gz",
+      "payload_equal": true,
+      "payload_sha256": "cc8e27b329defb34e5fe89bc18f886a4c9ff0f99a08bd4f686f4298b0eb39e04",
+      "present": true
+    },
+    {
+      "canonical_equal": true,
+      "container_sha256_new": "615093190aa5479034bb8acdd8925d7a910e082b84dec7df84b459b62421235a",
+      "container_sha256_old": "615093190aa5479034bb8acdd8925d7a910e082b84dec7df84b459b62421235a",
+      "file": "FOUR-extra.json.gz",
+      "payload_equal": true,
+      "payload_sha256": "c517eed7547e48ddc9f1f561e2fcc436b5999dab4aeb0cc634806c910d5444fc",
+      "present": true
+    }
+  ],
+  "word_law_later": {
+    "rank2_constant": true,
+    "rank48_is_idle48": true,
+    "rank5_is_word_plus_idle5": true,
+    "rank8_constant": true,
+    "residuals_ok": true,
+    "x": 1090,
+    "x_consistent": true,
+    "x_rank1": "1090",
+    "x_rank3": "1090",
+    "x_rank4": "1090"
+  },
+  "word_law_pinned": {
+    "rank2_constant": true,
+    "rank48_is_idle48": true,
+    "rank5_is_word_plus_idle5": true,
+    "rank8_constant": true,
+    "residuals_ok": true,
+    "x": 1080,
+    "x_consistent": true,
+    "x_rank1": "1080",
+    "x_rank3": "1080",
+    "x_rank4": "1080"
+  },
+  "word_profile_anchors": {
+    "ceil_proof_has_L3": true,
+    "ceil_proof_has_delta": true,
+    "derived_L4_matches": true,
+    "mix_readme_has_four": true,
+    "mix_readme_has_three": true
+  }
+}

research/fourth-entry-ceiling-transfer/SOURCES.json

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+}