# Observation horizon — claim and evidence ledger

Companion to [When the Loop Must Wait](../when-the-loop-must-wait.md). This is a bounded historical and mathematical investigation, not a systematic literature review or an empirical test of Circulatory Epistemology. It develops the sensor's comparison of Galileo's short observing horizon with inquiry across greater distance and mediation.

## What supports each claim

| ID | Claim | Support inspected | Status and boundary |
|---|---|---|---|
| OH-01 | Galileo initially interpreted the points near Jupiter as fixed stars; subsequent configurations changed that interpretation. | *Sidereus Nuncius*, 7–11 January narrative, pp. 64–67 in the [Van Helden translation excerpt](https://bertie.ccsu.edu/naturesci/Cosmology/GalileoStarry.html). | Primary text in translation. His initial orbital conclusion occurs in the 11 January entry; the first simultaneous sight of four bodies is recorded on 13 January. These are different achievements. |
| OH-02 | Initial recognition of orbital motion and determination of orbital periods had different evidence requirements. | Same primary text, pp. 64 and 83–84. [Museo Galileo](https://www2.museogalileo.it/it/biblioteca-e-istituto-di-ricerca/progetti/incontra-galileo/31-opere/454-sidereus-nuncius-1610.html) locates the published positions at 7 January–2 March. | Historical support. The nearly two-month published record is not the time until the initial inference. The existing CE passage already includes multiple nights; this note develops it rather than correcting an alleged instantaneous observation. |
| OH-03 | Saturn's triple appearance was an ambiguous telescopic appearance, not an identified physical ring. | [Galileo Project at Rice](https://galileo.library.rice.edu/sci/observations/saturn.html), the 1610 letter, 1612 disappearance and 1616 appearance; [Huygens' retrospective account](https://mathshistory.st-andrews.ac.uk/Extras/Huygens_Saturn/). | Specialist historical account and primary text in translation. Observed appearance and inferred constitution differ; Galileo's proposed explanations were not all correct. |
| OH-04 | Huygens combined improved optics, successive appearances and geometrical reasoning; his ring hypothesis predates its full 1659 publication. | [*Systema Saturnium* translated extracts](https://mathshistory.st-andrews.ac.uk/Extras/Huygens_Saturn/), lens making, the 1656 anagram and the changing projected ring. | Primary text in translation, excerpted. The Museo summary's wording that he first formed the hypothesis in 1659 is imprecise. The translation dates the encoded announcement to March 1656 with a day-of-month discrepancy; no exact day is claimed. The full Latin book was not inspected. |
| OH-05 | An artificial ringed Saturn viewed through different telescopes could reproduce the triple appearance. | [Museo Galileo, “Saturn's system”](https://catalogue.museogalileo.it/multimedia/SaturnsSystemBis.html), the Accademia del Cimento's 1660 model experiment. | Specialist institutional account, not independently repeated here. This demonstrates an optical possibility, not unique proof of the real planet's structure. |
| OH-06 | Light-travel time and the interval needed to discriminate hypotheses are different. | [NASA Webb explanation](https://science.nasa.gov/mission/webb/science-overview/science-explainers/how-does-webb-see-back-in-time/) supports finite light travel and seeing a past state. [Exact model](model.py) separates source and receipt epochs. | Physical background plus an idealized illustration. Distance imposes no universal monotonic law on inference time. The model assumes known constant delay, not a cosmological distance approximation. |
| OH-07 | Fresh observations can be redundant; a later view can distinguish candidates when its measurement operator changes. | [model.py](model.py), `test_model.py`, [results.json](results.json). | Exact for two objects, noiseless scheduled sum/difference views and known orientation. Repeated noisy observations can improve precision under an appropriate noise model. The schedule is engineered, not orbital mechanics. |
| OH-08 | Unknown fixed left/right wiring leaves both objects compatible with every scheduled view; a known reference can resolve that ambiguity. | Same model. Swapping both object and wiring leaves all scheduled measurements unchanged. Tests assert the exact surviving pair for both parity cases, both objects and both wiring states. | The all-epoch claim follows from the operator's two parity cases and their swap symmetry. Calibration requires a known reference, stable wiring and a difference view. A reference in the sum view cannot resolve the swap. |
| OH-09 | Reinterpreting an archive can reveal an implication without supplying independent confirmation. | The toy's repeated-record case adds no constraint. [Dwork et al., reusable holdout](https://research.ibm.com/publications/the-reusable-holdout-preserving-validity-in-adaptive-data-analysis) addresses dependence when analyses adapt to prior results. | The paper was inspected at its primary author/institution abstract, not replicated. Protected reuse can be valid. Archival age alone neither invalidates evidence nor establishes independence. The noiseless toy does not test adaptive statistics. |
| OH-10 | Human presence alone cannot establish that a particular update received corrective evidence about its target. | [The Veer](/appendices/the-veer), the “every free-energy reduction is grounded” passage and sensor-presence proxy. OH-07/08 supply nondiscriminating channels. | A challenge to the operational proxy. A signal can constrain total brightness without distinguishing left from right. The toy does not compute transfer entropy or validate free-energy equations. A detector receiving evidence is not thereby a living experiencer. |
| OH-11 | A loop should preserve possible correction across the time and mediation its claim requires. | Synthesis of the sensor's proposal, OH-01–10 and the framework's living-recognition thesis. | Proposed epistemic discipline, not a theorem, guarantee of closure or demonstrated advantage over existing methods. The living-recognition thesis remains philosophical; the toy neither proves it nor equates discrimination with recognition. |

## What the proposed rule asks for

For a particular claim, name the alternatives, the record already held, the instrument assumptions, and the observation that could separate those alternatives. Distinguish the time the source was sampled from the time the record arrived and the time its implication was recognized. Then choose interpretation, another acquisition, calibration, or waiting for a specified opportunity. The choices can be combined. If no feasible observation can distinguish the candidates, retain an unresolved result; elapsed time and engagement do not certify closure.

Noisy cases would need likelihoods, costs and a justified threshold; exact equality in the toy does not supply these. Unknown alternatives and a wrong instrument model remain possible even when a named set has been separated. This is an investigative rule, not yet an implemented general acquisition policy.

The three earlier threads require different controls. Imaging needs a measurement that distinguishes structures. Adaptive analysis must account for how the claim was selected and protect its evaluation. Performative prediction must distinguish the response under each action from the outcome generated by the action actually taken. None follows merely from another conversation turn.

## Reproduce and assess

From the repository root:

```bash
python3 -m unittest discover -s research/observation-horizon -p 'test_*.py' -v
python3 research/observation-horizon/model.py --output research/observation-horizon/results.json
```

The JSON records compatible objects and instrument states, not recognition scores. There is no randomness, learned reconstruction, human participant experiment or numerical transfer-entropy estimate. Tests cover both objects, both wiring states, repeated and delayed observations, and the stated calibration assumption.

An eventual empirical comparison would hold acquisition opportunities and costs constant and compare the proposed rule against existing experimental-design and causal-inference procedures. Outcomes could include false structures accepted, missed structures, time to identify instrument ambiguity and uncertainty calibration. No such comparison has been run. This package is a candidate formulation with exact counterexamples to overly broad proxies.

No published source or site mirror is changed by this research package. A repair to the Veer's grounding claims requires its own claim/equation/mirror pass; this note records the precise unresolved target.