{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:TO7JPWFISEGZE3AHX5C5ULQ5AC","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"7166f3cea8a7d780c48494968ff45d888aa820fb7b087dbe236e9505df613437","cross_cats_sorted":["cs.AI"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2026-07-06T10:55:56Z","title_canon_sha256":"d5468f397188aabd1b763fdae15f325c4256601210abfcfbbd988878d003e9a6"},"schema_version":"1.0","source":{"id":"2607.04926","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.04926","created_at":"2026-07-07T02:20:13Z"},{"alias_kind":"arxiv_version","alias_value":"2607.04926v1","created_at":"2026-07-07T02:20:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.04926","created_at":"2026-07-07T02:20:13Z"},{"alias_kind":"pith_short_12","alias_value":"TO7JPWFISEGZ","created_at":"2026-07-07T02:20:13Z"},{"alias_kind":"pith_short_16","alias_value":"TO7JPWFISEGZE3AH","created_at":"2026-07-07T02:20:13Z"},{"alias_kind":"pith_short_8","alias_value":"TO7JPWFI","created_at":"2026-07-07T02:20:13Z"}],"graph_snapshots":[{"event_id":"sha256:1765272bfc0e1934c2a7472e0558d174ea18a26e7e7ecb817c26b34b2bdd9c6c","target":"graph","created_at":"2026-07-07T02:20:13Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2607.04926/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"How does the way information reaches a transformer -- as symbolic tokens, a clean per-factor \"oracle\" code, or an entangled perceptual vector -- shape whether it binds that information compositionally? We study ~6-10K-parameter transformers on finite factored worlds enumerated exhaustively, so every measurement covers the whole input space (zero sampling variance) and the informative routes are information-matched (exact Bayes ceiling 1.0). We report four findings. (1) Endpoint invariance: on held-out binding queries no informative route reaches converged zero-shot composition -- each ends at ","authors_text":"Yoshiyuki Ootani","cross_cats":["cs.AI"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2026-07-06T10:55:56Z","title":"Input Pathways Shape Few-Shot, Not Zero-Shot, Binding in Tiny Transformers: A Fully-Enumerable Study"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.04926","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:470ac0cf1251f1f499985dca34ec792015390913823ebc0820b99255b3bd839b","target":"record","created_at":"2026-07-07T02:20:13Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"7166f3cea8a7d780c48494968ff45d888aa820fb7b087dbe236e9505df613437","cross_cats_sorted":["cs.AI"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2026-07-06T10:55:56Z","title_canon_sha256":"d5468f397188aabd1b763fdae15f325c4256601210abfcfbbd988878d003e9a6"},"schema_version":"1.0","source":{"id":"2607.04926","kind":"arxiv","version":1}},"canonical_sha256":"9bbe97d8a8910d926c07bf45da2e1d009450a65bb526b164ec33bab5da0a3192","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9bbe97d8a8910d926c07bf45da2e1d009450a65bb526b164ec33bab5da0a3192","first_computed_at":"2026-07-07T02:20:13.061779Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-07T02:20:13.061779Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"aMilS6OVLdiwzbrACFbI8nomyQTyqobcHy2CbRLCTa4rm7eIJfQH3RjpT/ok12TeFYtb3diikPeWnQf2maBVCg==","signature_status":"signed_v1","signed_at":"2026-07-07T02:20:13.062504Z","signed_message":"canonical_sha256_bytes"},"source_id":"2607.04926","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:470ac0cf1251f1f499985dca34ec792015390913823ebc0820b99255b3bd839b","sha256:1765272bfc0e1934c2a7472e0558d174ea18a26e7e7ecb817c26b34b2bdd9c6c"],"state_sha256":"6d7a5f845005c4c162e709b6fc4ff69b934b3fc7363a71d555f8e8f760cafd59"}