# Observer models and research threads · 1.45

These are bounded mathematical models motivated by Hoffman-related research,
not empirical discoveries about consciousness or a complete implementation of
conscious realism. The dated primary references and their publication status
are listed in `/threads/sources.mjs` and the workbench.

## Six models

- `observer_ab`: row-stochastic four-state cyclic/uniform mixture. Eliminate
  hidden states with a linear hitting solve, independently accumulate the
  first-return series, check the conditional uniform stationary distribution,
  and compare separate seeded trajectories with a union-bound Hoeffding limit.
  A first return requires at least one primitive transition.
- `nested_trace`: a four-state chain contains an absorbing hidden state.
  Only hidden states that can reach the observation set enter the solve.
  Missing probability is nonreturn, not renormalized successful returns.
  At leakage 1/4 the outer trace is [[1/4,5/8],[5/8,1/16]];
  the trace onto state 0 is 2/3 and nonreturn is 1/3. Direct and nested traces
  agree. Unconditional return time is infinite; no finite mean is reported.
- `hidden_clock`: visible kernel [[.8,.2],[.3,.7]] with geometric hidden waits.
  Each event costs 1+Geom(q) primitive transitions, with expectation 1+1/q.
  Event laws coincide; timestamp laws do not. Sampled strings are not claimed
  identical, and no computational speedup is inferred from hiding operations.
- `adaptive_window`: iid Bernoulli(p) raw states, the same fixed raw-step budget
  for both observers. After 0 wait for 1; after 1 accept the next state. The
  event kernel is [[0,1],[1-p,p]], stationary P(1)=1/(2-p). The window is frozen
  during waiting, with the first 32 event policies recorded. Trailing wait is
  censored, not nonreturn. This is inspired by RTL, not the full meta-policy.
- `fitness_truth`: enumerate all 16 one-bit encoders and four decoders on four
  equiprobable states. Reward mixes coordinate-bin and parity tasks. Coordinate
  distortion is 1/4 versus parity's 1; both balanced codes retain one bit.
  Full information with an optimal decoder can emulate the best coarse policy.
  Explicit bit costs separate gross and net utility. There is no universal
  claim that truth loses to fitness.
- `quantum_instrument`: real qubit density matrices, Lüders Z versus Z followed
  by preparation of |+>. Equal effects imply equal first probabilities, while
  repeated-outcome probability is 1 versus 1/2. Verify Kraus completeness,
  positivity, normalization and sequential probabilities. Impossible branches
  have null conditional state. Born probabilities are assumed, not derived.

All seeds, bounds and tolerances are frozen in catalog/core sources. A Monte
Carlo discrepancy can fail a run; it is never coerced into a passing status.
Power-series controls and exact identities supplement same-code replay; they
are not external scientific replication. No arbitrary code or URLs execute.

## Runtime threads and storage

`GET /api/runtime/threads` returns three fixed DAGs. `POST
/api/runtime/threads/run` accepts only `{"thread":"observation"}` (or
`adaptation`, `measurement`), JSON ≤256 bytes with same-origin Origin header.
No custom parameters, jobs, paid APIs, external agents or schedules are created.
Each frozen plan includes defaults, source hashes, criteria and scope. The
execution key is the plan hash plus the server-hour slot. The existing D1
`runtime_runs` table stores full plans, all step results, failures, dependency
hashes and evidence graphs. GET `/api/runtime/threads/runs` lists ≤30 rows;
`/api/runtime/runs/{id}` returns persisted evidence. No lease tokens are public.

Leases expire after 30 seconds with at most three attempts. The unique owner
token fences completion after takeover. A completed row is immutable. Duplicate
requests return the stored row; this promises one committed result, not exactly
one computation after a crash. Fixed work and output are bounded; a failed
required step blocks descendants. Links are scientific review prerequisites,
not equations deriving a later model from an earlier model's output. Server
roles run in one process; they are not independent agents.

Parameterized workbench runs instead use the existing signed BrowserEngine,
origin-scoped IndexedDB and exportable evidence. Local signatures attest bytes,
not a real person or scientific truth. The server does not ingest browser claims
as verified facts. All six recipes also run without network in Node/SQLite:

```sh
node scripts/run-catalog.mjs --recipe observer_ab --db data/research.sqlite
node scripts/run-catalog.mjs --db data/research.sqlite
```

## Open research

The eight physics goals remain open source-linked directions. The DMT paper is
listed as a hypothesis and has no human-subject experiment or external-entity
verification in this runtime. New evidence would require a frozen independent
protocol, data provenance, leakage controls and model comparison. None of the
six toys substitutes for those measurements or domain review.

## Entropy and clock units — checked 2026-10-05

The fixed `hidden_clock` result also reproduces the counterexample in Trace Institute's undated working paper [Trace Logic and Theory of Computation](https://www.traceinstitute.org/papers/working/trace-logic-and-computation.pdf), §6.6, Example 6.7. For `Q=[[0,1,0],[1/2,0,1/2],[1,0,0]]` and visible states `{0,2}`, the return kernel is `P=[[1/2,1/2],[1,0]]`. Stationary distributions are `(2/5,2/5,1/5)` and `(2/3,1/3)`. Entropy rates are `2/5` bits/raw step and `2/3` bits/event. An event costs `5/3` raw steps on average; dividing by that cost returns `2/5` for this fixture. This disproves unconditional native-step entropy monotonicity under tracing, not physical thermodynamics. It does not establish a universal clock-normalized equality or any consciousness claim.

The verifier checks the submitted matrices, distributions, costs and rates against independent finite-path and exact-fraction identities. Missing or altered fixtures fail. No new paid model, external agent or scientific experiment is invoked.