Bound rounded error on the two #5833 P104 words: 20-bit guard, envelope below 97B (no new κ)

research/p104-gauge-word-rounded-guards/README.md

@@ -0,0 +1,119 @@
+# Rounded-error guards for the two PR5833 P104 words
+
+**Finite certificate; no new κ.** Ali Romman's PR5833 emitted two complete
+P104 words with sharp ideal field amplification 96 (original scalar budget)
+and 2 (minimum). PR5838 proved a 20-bit completed-operation guard for the
+earlier PR5830 word, with peak 65,537. It also asked for the bound to be
+recomputed for a later gauge tradeoff word. This package does that for both
+PR5833 words, under PR5838's contract and its causal bound, used unchanged.
+
+| Word | Ideal peak | Causal guard | Final public error | Intermediate error | Field norm + error |
+|---|---:|---:|---:|---:|---:|
+| PR5830 (PR5838's result) | 65,537 | 20 | < 0.97754 B | < 26.903 B | < 65,563.91 B |
+| PR5833 budget word | 96 | **20** | < 0.97746 B | **< 0.97746 B** | **< 96.978 B** |
+| PR5833 minimum word | 2 | **20** | < 0.97746 B | **< 0.97746 B** | **< 2.978 B** |
+
+B bounds every initial field's Hilbert norm and u = 2^-guard. All bounds are
+exact rationals in `RESULT.json`; the table rounds them up.
+
+What changes:
+
+- **The final guard stays at 20 bits.** At guard 19 the causal bound on both
+  new words is above 1.955 B, as on PR5830's word. Lowering amplification by
+  factors of about 683 and 32,768 does not lower the accepted final guard.
+- **The intermediate error envelope falls from 26.9 B to below 0.978 B.**
+  On both new words the largest error bound at any instruction is the final
+  bound on public field 205. No intermediate field ever carries a larger
+  error bound than the outputs.
+- **The field-magnitude envelope falls from below 2^17 B to below 97 B and
+  3 B.** Read as fixed-point headroom (an inference, not a physical
+  representation proof), the integer part above B needs 7 bits on the budget
+  word and 2 bits on the minimum word, against 17 on PR5830's word, with the
+  same 20 fractional guard bits.
+
+The budget word keeps PR5833's original allowance (224,878 ≤ 224,880 scalar
+primitives). Its precision envelope is therefore 10 integer bits narrower than
+PR5830's word, at 24,332 more scalar primitives than PR5830's 200,546. That
+is the tradeoff PR5833 asked to price; this package supplies only its error
+side.
+
+## Contract and method
+
+Every physical `MOVE`, `ADD` and `SCALE` of the emitted word is a relative
+defect site with PR5838's allowance: local ideal input norm plus actual prior
+error feedback, times u. `COPY`, `INIT` and `CLEAR` are exact, as in PR5838.
+The emitted PR5833 words already contain every entry, exit and lowered
+`SCALE`, and neither word has an identity `SCALE`, so no site is virtual.
+PR5838's `transfer.ideal` supplies the weights and checks every arbitrary-input
+endpoint row. PR5838's `causal.bound` computes the forward bound with exact
+signed coefficient rows and upward-rounded 96-bit dyadic defect bounds. Both
+files are imported from `research/p104-gauge-error-covariance` without change.
+
+**Adapter control.** PR5838 runs its bound on a timeline that also numbers
+exact virtual identities. Applied to PR5830's emitted word with all physical
+`MOVE`/`ADD`/`SCALE` as sites, this adapter reproduces PR5838's recorded
+20-bit case exactly. That covers all public and owned final coefficients, the
+peak value and its field, and the 26,271 sites; only the peak's instruction
+index differs. This shows the site convention matches. It is not a re-check
+of PR5838.
+
+Four controls are rejected: a truncated budget word and a budget word with one
+doubled `SCALE` coefficient both fail the endpoint check. Guard 19 is not
+accepted. Omitting 1,000 sites changes the bound.
+
+## Reproduce
+
+From the repository root with CPython 3.12 and the standard library:
+
+```sh
+python3.12 -I -W error -B research/p104-gauge-word-rounded-guards/verify.py
+python3.12 -I -O -W error -B research/p104-gauge-word-rounded-guards/verify.py
+python3.12 -B scripts/research_package.py --package research/p104-gauge-word-rounded-guards
+```
+
+Each prints `PASS_P104_GAUGE_WORD_ROUNDED_GUARDS` and takes about 17 seconds
+locally. `--write` regenerates `RESULT.json`; the default mode requires the
+committed receipt to equal the recomputation byte for byte. Sparse checkouts
+need `research/p104-gauge-error-covariance` and
+`research/p104-priced-amplification`. The six live inputs are pinned by Git
+blob and SHA256 in `SOURCES.json`.
+
+## Limits
+
+- This is an upper bound under one worst-case contract. Sharpness at 20 bits
+  is **not** claimed for the new words. PR5838 shows that a MOVE/ADD-only
+  19-bit trace survives every field-constant signed scalar gauge of its base
+  word. Whether PR5833's words lie in that gauge class was not checked here.
+- Hardware rounding with stronger correlations may need fewer bits; PR5838's
+  contract allows independently adverse completed defects.
+- No rounded native child, COPY/reset machine, signed-record range, tape or
+  descriptor cost is built or charged. The five framework assumptions remain.
+  No κ, selected-frontier or admission change follows.
+
+## Open next questions
+
+1. **Is 20 sharp on the PR5833 words?** Transport PR5838's family adversary
+   (`FAMILY-ADVERSARY.json`) to each word, or show the words are field-constant
+   signed scalar gauges of PR5838's base word. The first step is to map each
+   PR5833 instruction to its base-word event and gauge ratio.
+2. **Does a narrower field envelope buy a cheaper physical word?** The budget
+   word needs 7 integer bits instead of 17. Price a fixed-point record at
+   27 total bits against 37 in the actual tape/descriptor tariff, including
+   the extra 24,332 scalar primitives. Physical record widths are not yet bound.
+3. **Can a gauge lower the final guard itself?** Both new words keep the final
+   public bound near 0.9775 B. That points at the output-side native MOVE/ADD
+   chain, not field amplification. The first step is the per-site share of
+   field 205's final bound.
+
+## Credit
+
+This package was produced by Nick Petalas. The completed-operation contract,
+causal bound, transfer method and 20-bit PR5830 result are Ali Romman's PR5838
+(`research/p104-gauge-error-covariance`), which credits the PR5819/5826/5831
+transfer method and the PR5830/5824/5822/5812 gauge lineage. The two emitted
+words and their sharp ideal peaks are Ali Romman's PR5833
+(`research/p104-priced-amplification`). All P104, native and compiler authors
+retained in those packages' notices are credited through them. The new
+contribution is the rounded-error guard and envelopes for the two PR5833
+words. Independent human and formal proof-kernel review are unclaimed.
+Apache-2.0.

research/p104-gauge-word-rounded-guards/RESULT.json

@@ -0,0 +1,166 @@
+{
+ "adapter_control": "PR5830 word, every physical MOVE/ADD/SCALE a site: 20-bit causal case equals PR5838 RESULT.json causal_cases[guard=20] in every final coefficient, the peak value, its field and the 26271 defect sites. Only the peak instruction index differs, because PR5838 also numbers exact virtual identities.",
+ "claim": "Finite certificate: under PR5838's completed-operation relative-error contract and causal bound, both PR5833 words accept a 20-bit guard; intermediate error stays below 0.978B and field norm plus error below 97B (budget word) and 3B (minimum word).",
+ "rejected_controls": [
+  "drop the last instruction of the budget word",
+  "double one SCALE coefficient of the budget word",
+  "accept guard 19 on the budget word",
+  "omit the last 1000 defect sites without changing the bound"
+ ],
+ "schema_version": 1,
+ "source_hashes": {
+  "research/p104-gauge-error-covariance/RESULT.json": "b8967e8aeca1d59addc8094526232bda4b144b8a85df319a043e82536d07be03",
+  "research/p104-gauge-error-covariance/causal.py": "779fc064fc26ecd2091552eb23761ffecaf8a689f8ff027853bc3e88d90e6256",
+  "research/p104-gauge-error-covariance/inputs/WORD.json.gz": "6a7467851c2a3bc8aee3a7018bcf15290848f040484cfbff5a97ca0773207e0a",
+  "research/p104-gauge-error-covariance/transfer.py": "618231ab4e144999a71622511bbd41c6a0fb32351c12340e65311084f4cf0a18",
+  "research/p104-priced-amplification/BUDGET-WORD.json.gz": "2d707ffa13d95182aa799097b2ef0a6a8bdad29814976c4e52f66af8d2e517ff",
+  "research/p104-priced-amplification/MINIMUM-WORD.json.gz": "5ecbb6533ea43dbbb4865d61d6953e4180c4ac796ee9a620c0f11f85cc82d549"
+ },
+ "unit": "B, the bound on every initial field Hilbert norm; u = 2^-guard",
+ "words": {
+  "pr5830_gauge_word": {
+   "defect_sites": 26271,
+   "field_norm_plus_error_bound": "20778030171283507118687820528136407/316912650057057350374175801344",
+   "final_public_bound": "1268907899307767744718911294017839/1298074214633706907132624082305024",
+   "ideal_peak": "65537",
+   "identity_scale_sites": 0,
+   "instructions": 26351,
+   "intermediate_error_at": [
+    24580,
+    349
+   ],
+   "intermediate_error_bound": "8525824494139547215461035454679/316912650057057350374175801344",
+   "least_causal_guard": 20,
+   "operation_counts": {
+    "ADD": 21685,
+    "CLEAR": 29,
+    "COPY": 22,
+    "INIT": 29,
+    "MOVE": 3457,
+    "SCALE": 1129
+   },
+   "owned_fields": 12,
+   "public_fields": 770,
+   "rejected_final_public_bound": "317361194300804062733789640958015/162259276829213363391578010288128",
+   "rejected_guard": 19,
+   "scan": [
+    {
+     "final_public_bound": "1268505349529775942440067171376851/5192296858534827628530496329220096",
+     "guard": 22,
+     "intermediate_error_bound": "4262490850044930134848577591973/633825300114114700748351602688"
+    },
+    {
+     "final_public_bound": "2537279044886802426282421954976059/5192296858534827628530496329220096",
+     "guard": 21,
+     "intermediate_error_bound": "8525262622353040458504352712329/633825300114114700748351602688"
+    },
+    {
+     "final_public_bound": "1268907899307767744718911294017839/1298074214633706907132624082305024",
+     "guard": 20,
+     "intermediate_error_bound": "8525824494139547215461035454679/316912650057057350374175801344"
+    },
+    {
+     "final_public_bound": "317361194300804062733789640958015/162259276829213363391578010288128",
+     "guard": 19,
+     "intermediate_error_bound": "17053896693521503963650793986429/316912650057057350374175801344"
+    }
+   ]
+  },
+  "pr5833_budget_word": {
+   "defect_sites": 27022,
+   "field_norm_plus_error_bound": "491734110945483183559404247863187/5070602400912917605986812821504",
+   "final_public_bound": "4956280457843093384670216998803/5070602400912917605986812821504",
+   "ideal_peak": "96",
+   "identity_scale_sites": 0,
+   "instructions": 27102,
+   "intermediate_error_at": [
+    26539,
+    205
+   ],
+   "intermediate_error_bound": "4956280457843093384670216998803/5070602400912917605986812821504",
+   "least_causal_guard": 20,
+   "operation_counts": {
+    "ADD": 21685,
+    "CLEAR": 29,
+    "COPY": 22,
+    "INIT": 29,
+    "MOVE": 3457,
+    "SCALE": 1880
+   },
+   "owned_fields": 12,
+   "public_fields": 770,
+   "rejected_final_public_bound": "9916780791124075418200791780253/5070602400912917605986812821504",
+   "rejected_guard": 19,
+   "scan": [
+    {
+     "final_public_bound": "309668651851752592698620988495/1267650600228229401496703205376",
+     "guard": 22,
+     "intermediate_error_bound": "309668651851752592698620988495/1267650600228229401496703205376"
+    },
+    {
+     "final_public_bound": "619403216486029567696652192465/1267650600228229401496703205376",
+     "guard": 21,
+     "intermediate_error_bound": "619403216486029567696652192465/1267650600228229401496703205376"
+    },
+    {
+     "final_public_bound": "4956280457843093384670216998803/5070602400912917605986812821504",
+     "guard": 20,
+     "intermediate_error_bound": "4956280457843093384670216998803/5070602400912917605986812821504"
+    },
+    {
+     "final_public_bound": "9916780791124075418200791780253/5070602400912917605986812821504",
+     "guard": 19,
+     "intermediate_error_bound": "9916780791124075418200791780253/5070602400912917605986812821504"
+    }
+   ]
+  },
+  "pr5833_minimum_word": {
+   "defect_sites": 27027,
+   "field_norm_plus_error_bound": "117949169803671572367362214249/39614081257132168796771975168",
+   "final_public_bound": "38721007289407234773818263913/39614081257132168796771975168",
+   "ideal_peak": "2",
+   "identity_scale_sites": 0,
+   "instructions": 27107,
+   "intermediate_error_at": [
+    26540,
+    205
+   ],
+   "intermediate_error_bound": "38721007289407234773818263913/39614081257132168796771975168",
+   "least_causal_guard": 20,
+   "operation_counts": {
+    "ADD": 21685,
+    "CLEAR": 29,
+    "COPY": 22,
+    "INIT": 29,
+    "MOVE": 3457,
+    "SCALE": 1885
+   },
+   "owned_fields": 12,
+   "public_fields": 770,
+   "rejected_final_public_bound": "309899930218753983333898480473/158456325028528675187087900672",
+   "rejected_guard": 19,
+   "scan": [
+    {
+     "final_public_bound": "38708647619431921159920415107/158456325028528675187087900672",
+     "guard": 22,
+     "intermediate_error_bound": "38708647619431921159920415107/158456325028528675187087900672"
+    },
+    {
+     "final_public_bound": "77425534386359887694650009247/158456325028528675187087900672",
+     "guard": 21,
+     "intermediate_error_bound": "77425534386359887694650009247/158456325028528675187087900672"
+    },
+    {
+     "final_public_bound": "38721007289407234773818263913/39614081257132168796771975168",
+     "guard": 20,
+     "intermediate_error_bound": "38721007289407234773818263913/39614081257132168796771975168"
+    },
+    {
+     "final_public_bound": "309899930218753983333898480473/158456325028528675187087900672",
+     "guard": 19,
+     "intermediate_error_bound": "309899930218753983333898480473/158456325028528675187087900672"
+    }
+   ]
+  }
+ }
+}

research/p104-gauge-word-rounded-guards/SOURCES.json

@@ -0,0 +1,72 @@
+{
+  "schema_version": 1,
+  "base_commit": "19fdb086ea96af9a9f87936a2b888e10af4ed810",
+  "files": [
+    {
+      "path": "certificates/selected-result.json",
+      "usage": "provenance",
+      "git_blob": "581f8d87008354eb5b869f7ed9de1317ad837ce8",
+      "sha256": "2a0220e866417774606e0f991e41b9c1d26b1f43b97857238cf478dbc7d330b5"
+    },
+    {
+      "path": "docs/research/agent-task-catalog.json",
+      "usage": "provenance",
+      "git_blob": "3404fbdd5e7529a0674eef26114b5071e4586cec",
+      "sha256": "ead6cdc9d0af6d58e8a49744d8ec8c7c15e13d2ba93c276c434bcf9b51b93a81"
+    },
+    {
+      "path": "research/p104-gauge-error-covariance/README.md",
+      "usage": "provenance",
+      "git_blob": "6e32f5c58c390d32fa2d72f1bf72fcdf2151d4d6",
+      "sha256": "0c621274810b65505f86f574efabf2568f8fca74a509af9129b55173451bdadd"
+    },
+    {
+      "path": "research/p104-gauge-error-covariance/PROOF.md",
+      "usage": "provenance",
+      "git_blob": "a063d07914fdb231deed44ec9f46867663704da3",
+      "sha256": "42a384aecb898734cb1f80576733e88938815e79244a99e5c69e766c0c3cbd64"
+    },
+    {
+      "path": "research/p104-priced-amplification/README.md",
+      "usage": "provenance",
+      "git_blob": "6b0b14e9bfb2b6340a3583fc5bf54a09e3054206",
+      "sha256": "15cfbc92e2542ff9fe42f8cbf30a54ab9bf4b778ae5d4bbcc725438c064971ff"
+    },
+    {
+      "path": "research/p104-gauge-error-covariance/causal.py",
+      "usage": "input",
+      "git_blob": "4e0b39a1122ff6e16a49461e07f33f38634596ca",
+      "sha256": "779fc064fc26ecd2091552eb23761ffecaf8a689f8ff027853bc3e88d90e6256"
+    },
+    {
+      "path": "research/p104-gauge-error-covariance/transfer.py",
+      "usage": "input",
+      "git_blob": "5c50ea955278dcddf1127e83cbbbd3751fbcdc2d",
+      "sha256": "618231ab4e144999a71622511bbd41c6a0fb32351c12340e65311084f4cf0a18"
+    },
+    {
+      "path": "research/p104-gauge-error-covariance/RESULT.json",
+      "usage": "input",
+      "git_blob": "001384efbb813cf507e991aa89cf79a9dd1ab190",
+      "sha256": "b8967e8aeca1d59addc8094526232bda4b144b8a85df319a043e82536d07be03"
+    },
+    {
+      "path": "research/p104-gauge-error-covariance/inputs/WORD.json.gz",
+      "usage": "input",
+      "git_blob": "3b04755eef3733505d2a81b477215936dcb9564e",
+      "sha256": "6a7467851c2a3bc8aee3a7018bcf15290848f040484cfbff5a97ca0773207e0a"
+    },
+    {
+      "path": "research/p104-priced-amplification/BUDGET-WORD.json.gz",
+      "usage": "input",
+      "git_blob": "b154eb8768f4f956ffd5d099993c4bd8f101a6cf",
+      "sha256": "2d707ffa13d95182aa799097b2ef0a6a8bdad29814976c4e52f66af8d2e517ff"
+    },
+    {
+      "path": "research/p104-priced-amplification/MINIMUM-WORD.json.gz",
+      "usage": "input",
+      "git_blob": "075fbbca0e8548fc7b9048491f30debe5ddf48f3",
+      "sha256": "5ecbb6533ea43dbbb4865d61d6953e4180c4ac796ee9a620c0f11f85cc82d549"
+    }
+  ]
+}