research(pcea): gate gonol interpolation prediction

Author: erinepshovel-code

research/pcea/ACTOR_A_ASYNC_GONOL_RESULT.md

@@ -2,6 +2,23 @@
 
 **Standing:** research result, not PCEA runtime, not UCNS canon, not a public-key or hardness claim.
 
+## 2026-09-01 provenance refresh
+
+Stack branch `research/pcea-async-gonol-keys-a` was refreshed from prior Actor A commit `ce41ceb86b0e4819bfbb976f3ce187567391af48` and merged with stack `origin/main@04253ab5bed7e913ab3df7bbb00939340bca291e`, producing branch parent `675836eef7bbcdaaa2edc4f8246591617e161955` before this refresh commit.
+
+Current exact authority identities checked:
+
+```text
+stack/libs/pcea pinned source = The-Interdependency/pcea@91ffa8c7249dfb810ca64a0bbc500481c0bd12a9
+PCEA live main = The-Interdependency/pcea@834987cb0c1fea5f62d6ea08e5c5bb878c312646
+stack/libs/ucns pinned source = The-Interdependency/ucns@1975fe70cf4e0826a8020c2da3047569e277af64
+UCNS live main = The-Interdependency/ucns@cff04c85df5a56fd3f9d3b178e7c49160d749652
+UCNS public_gonol.py blob = c1955e46e2dc918fb657cb346e42106d71937e91
+PCEA pyproject.toml blob = a4c2d9449c77765c0698afb869ecfd08bc1c5483
+```
+
+The relevant UCNS Public Gonol carrier blob remains unchanged between the stack-pinned UCNS snapshot and live UCNS main. Live UCNS `CANON.md` still records the full recursive-scale transition law as `hmmm`; no actual recursive UCNS gonol constructor value for the next step was available.
+
 ## Source recovery
 
 Actor A checked the refreshed stack boundary and materialized the exact legacy PCEA research lane from `The-Interdependency/pcea@ecf2ca0dec38bef29382e02121b0edde66763aa9`. The legacy materializer verified 36 files, including `pcea-ucns/gonal_architecture.py` at blob `a24e31110521b30ca941bf151b99458a06c910af`.
@@ -14,9 +31,9 @@ No source-level recursive gonol transition operator for:
 
 was present in the current stack refresh, the pinned UCNS authority, or the migrated PCEA research lane. UCNS still records the full recursive-scale transition law as `hmmm`.
 
-## Frozen operator
+## Interpolation baseline
 
-The exact operator recoverable from the available evidence is therefore an observation-index candidate:
+The exact replay baseline recoverable from the available evidence is therefore an observation-index interpolation candidate:
 
 ```text
 operator_id = pcea.async_gonol.observation_second_difference.v1
@@ -34,13 +51,13 @@ y_1 = 2881
 y_2 = 54837698421
 ```
 
-and derives the next candidate gonol:
+and predicts the next candidate gonol:
 
 ```text
 y_3 = 164513086777
 ```
 
-This next value is a falsifiable research coordinate under the frozen candidate operator. It is not promoted as the UCNS recursive-scale law.
+This next value is frozen as a prediction under the interpolation baseline. It is not promoted as the UCNS recursive-scale law and must be compared with the actual UCNS constructor output once that constructor exists.
 
 ## Lazy key-state candidate
 
@@ -64,42 +81,61 @@ The root secret is the only entropy-bearing input. Gonol size, geometry, path, p
 The test suite exercises:
 
 - exact replay of `157 -> 2881 -> 54837698421`;
-- derivation of `164513086777` under the named candidate operator;
+- prediction of `164513086777` under the named interpolation baseline;
+- unresolved actual-UCNS constructor status and the match/mismatch comparison rule;
 - lazy single-coordinate derivation without expanding the gonol;
 - key changes when path, state, transcript, position, or message counter changes;
 - out-of-order receive support by address;
 - replay rejection by receiver-side coordinate cache;
-- comparison guardrails that keep the security basis external to gonol geometry.
+- deferral of linear/tree/gonol key-addressing comparison until the out-of-sample UCNS value exists.
 
-## Comparison
+## Out-of-sample gate
 
-Against an ordinary linear ratchet, the gonol-addressed candidate has better natural out-of-order derivation because the receiver can derive from public path/position/epoch/message coordinates. Replay protection is not inherent; it requires a coordinate cache or equivalent nonce discipline.
+The actual UCNS recursive gonol constructor is still unresolved. The current comparison state is:
 
-Against an ordinary tree KDF, the candidate is similar: both can derive sparse branches lazily. No compromise-containment advantage is credited to gonol geometry. Containment still depends on root-secret separation, subkey erasure, and ratcheting policy.
+```text
+actual_next_gonol = hmmm
+prediction = 164513086777
+baseline_outcome = UNRESOLVED
+```
+
+When the actual UCNS constructor supplies a next value:
+
+```text
+actual != 164513086777 -> quadratic/interpolation candidate FALSIFIED
+actual == 164513086777 -> SURVIVED one out-of-sample test
+```
 
-Recovery is promising only as an addressability feature: path and state receipts can help a receiver resynchronize, but the public metadata itself becomes an attack surface for linkability and state leakage.
+The linear/tree/gonol key-addressing comparison is deferred until that out-of-sample gate resolves. When it runs, all schemes must use the same standard KDF and root entropy; gonol size or geometry still does not contribute entropy or hardness.
 
 ## Freeze receipt
 
 Generated evidence:
 
 ```text
 research/pcea/async_gonol_key_state_freeze.json
-receipt_digest = cbc1343a69bc3b72a93351348ab0cba4962b25d06cd27bc9450f722a4f11814f
+schema = pcea.async-gonol-key-state.freeze.v2
+receipt_digest = e15e34b8dde02088ca74502ae2d583d6f0b273c298e5e690fe4030668bffdcee
 ```
 
 Source identities bound in the receipt:
 
 ```text
-pcea_cleanup_commit = 91ffa8c7249dfb810ca64a0bbc500481c0bd12a9
-stack_refresh_commit = eaec7fd6ee4e829b6fae10a2c6d520b35857137d
+pcea_stack_pinned_commit = 91ffa8c7249dfb810ca64a0bbc500481c0bd12a9
+live_pcea_main_commit = 834987cb0c1fea5f62d6ea08e5c5bb878c312646
+ucns_stack_pinned_commit = 1975fe70cf4e0826a8020c2da3047569e277af64
+live_ucns_main_commit = cff04c85df5a56fd3f9d3b178e7c49160d749652
+stack_pcea_refresh_commit = eaec7fd6ee4e829b6fae10a2c6d520b35857137d
+stack_origin_main_at_refresh = 04253ab5bed7e913ab3df7bbb00939340bca291e
+stack_branch_parent_at_refresh = 675836eef7bbcdaaa2edc4f8246591617e161955
+prior_actor_a_commit = ce41ceb86b0e4819bfbb976f3ce187567391af48
 legacy_research_source_commit = ecf2ca0dec38bef29382e02121b0edde66763aa9
 pinned_public_gonol_sha256 = 55d10c84529a4d7bc7714786357e977b68d9df2ac3f73d20e229580b552c2ef5
 ```
 
 ## hmmm
 
 - Exact UCNS recursive-scale transition law remains unresolved.
-- `164513086777` is only the next value under the frozen observation candidate.
+- `164513086777` is only a prediction under the frozen interpolation baseline.
 - Any public-authenticity layer still requires normal signatures, MACs, transparency logs, timestamps, and receipt verification outside this candidate.
 - Any deployment would need attack review for metadata leakage, skipped-coordinate exhaustion, replay cache persistence, state-loss recovery, and compromise recovery.

research/pcea/ASYNC_GONOL_KEYS.md

@@ -56,7 +56,7 @@ Public coordinates may identify where a receiver should derive; they must not su
 
 Actor A materialized and verified the legacy PCEA research lane, then searched the current stack refresh, pinned UCNS authority, and migrated PCEA research files. No source-level UCNS recursive-scale transition operator for `157 -> 2881 -> 54837698421` was present.
 
-The frozen executable result is therefore an observation-index candidate:
+The frozen executable result is therefore an observation-index interpolation baseline:
 
 ```text
 operator_id = pcea.async_gonol.observation_second_difference.v1
@@ -72,13 +72,13 @@ It independently replays:
 157 -> 2881 -> 54837698421
 ```
 
-and derives:
+and predicts:
 
 ```text
 next = 164513086777
 ```
 
-This is not a UCNS recursive-scale law. It is a falsifiable replay/next-step candidate for further attack.
+This is not a UCNS recursive-scale law. It is a falsifiable prediction for the next out-of-sample UCNS constructor value.
 
 Executable artifacts:
 
@@ -91,10 +91,38 @@ ACTOR_A_ASYNC_GONOL_RESULT.md
 
 The lazy key schedule derives one traffic key per address/path/state coordinate with HMAC-SHA256 over caller-supplied root secret plus public synchronization context. The root secret remains the only entropy-bearing input.
 
+## 2026-09-01 refresh
+
+Current exact live authority checks:
+
+```text
+PCEA live main = 834987cb0c1fea5f62d6ea08e5c5bb878c312646
+UCNS live main = cff04c85df5a56fd3f9d3b178e7c49160d749652
+stack origin/main at refresh = 04253ab5bed7e913ab3df7bbb00939340bca291e
+```
+
+Stack still pins PCEA at `91ffa8c7249dfb810ca64a0bbc500481c0bd12a9` and UCNS at `1975fe70cf4e0826a8020c2da3047569e277af64`.
+
+The actual recursive UCNS gonol constructor remains unresolved in live UCNS. Therefore:
+
+```text
+actual_next_gonol = hmmm
+prediction = 164513086777
+baseline_outcome = UNRESOLVED
+linear/tree/gonol key-addressing comparison = DEFERRED
+```
+
+Once UCNS supplies the actual next value, compare it directly:
+
+```text
+mismatch -> interpolation candidate FALSIFIED
+match -> SURVIVED one out-of-sample test
+```
+
 ## Usage guidance
 
 Do not implement this in `The-Interdependency/pcea` while it remains candidate research. Prototype and attack it here. If a bounded ratchet behavior survives and is useful, promote only that completed behavior to PCEA through an explicit owning-repository change.
 
 ## hmmm
 
-The load-bearing unknown is still the exact UCNS recursive transition operator. Independent replay now exists for the supplied observation under a named observation-level candidate, but gonol scale remains a research coordinate, not cryptographic hardness, entropy, or canon.
+The load-bearing unknown is still the exact UCNS recursive transition operator. Independent replay now exists for the supplied observation under a named interpolation baseline, but gonol scale remains a research coordinate, not cryptographic hardness, entropy, or canon.

research/pcea/README.md

@@ -34,7 +34,9 @@ Do not edit `migrated/` as though it were current canon. Materialize a lane, the
 
 The current candidate line is asynchronous PCEA key orchestration over gonol state. The observed `157 -> 2881 -> 54837698421` progression is research evidence, not yet a cryptographic hardness claim or UCNS recursive-scale law.
 
-Actor A froze the observation-level replay in `async_gonol_keys.py`, generated `async_gonol_key_state_freeze.json`, and recorded the narrative in `ACTOR_A_ASYNC_GONOL_RESULT.md`. The independently replayed observation derives `164513086777` as the next candidate value under `pcea.async_gonol.observation_second_difference.v1`. That operator is a falsifiable observation candidate, not the unresolved UCNS recursive-scale law.
+Actor A froze the observation-level replay in `async_gonol_keys.py`, generated `async_gonol_key_state_freeze.json`, and recorded the narrative in `ACTOR_A_ASYNC_GONOL_RESULT.md`. The independently replayed observation predicts `164513086777` as the next candidate value under `pcea.async_gonol.observation_second_difference.v1`. That operator is a three-point interpolation baseline, not the unresolved UCNS recursive-scale law.
+
+The 2026-09-01 refresh found live PCEA at `834987cb0c1fea5f62d6ea08e5c5bb878c312646` and live UCNS at `cff04c85df5a56fd3f9d3b178e7c49160d749652`; the actual recursive UCNS gonol constructor is still unresolved, so the prediction's out-of-sample status is `UNRESOLVED` and linear/tree/gonol key-addressing comparison is deferred.
 
 PCEA keys must still derive from real secret entropy; gonol state may organize, address, ratchet, or synchronize that entropy but must not be credited with entropy merely because the address space is large.
 
@@ -49,5 +51,5 @@ PCEA keys must still derive from real secret entropy; gonol state may organize,
 
 ## hmmm
 
-- The exact UCNS recursive transition operator producing `157 -> 2881 -> 54837698421` is still not recovered; only a named observation-level replay candidate exists here.
+- The exact UCNS recursive transition operator producing `157 -> 2881 -> 54837698421` is still not recovered; only a named interpolation baseline exists here.
 - No independent cryptographic/security review is implied by this migration or by the PCEA runtime tests.