{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:5NAMPT2QNX53L3GPFSKRADWQ7T","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":"9e595ab93ea1b3ccdf4a2112a0ac3e35f79e1f12c017c30896335c0c34dd0ffd","cross_cats_sorted":["cs.IT","math.IT"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.AI","submitted_at":"2026-07-14T05:52:12Z","title_canon_sha256":"fa2d2d960dee4fc9564aa2fe53de62ea645d0f58d3679ec0990bfc2919293a36"},"schema_version":"1.0","source":{"id":"2607.14144","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.14144","created_at":"2026-07-17T00:20:53Z"},{"alias_kind":"arxiv_version","alias_value":"2607.14144v1","created_at":"2026-07-17T00:20:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.14144","created_at":"2026-07-17T00:20:53Z"},{"alias_kind":"pith_short_12","alias_value":"5NAMPT2QNX53","created_at":"2026-07-17T00:20:53Z"},{"alias_kind":"pith_short_16","alias_value":"5NAMPT2QNX53L3GP","created_at":"2026-07-17T00:20:53Z"},{"alias_kind":"pith_short_8","alias_value":"5NAMPT2Q","created_at":"2026-07-17T00:20:53Z"}],"graph_snapshots":[{"event_id":"sha256:93f24fe9e99e3747eeef6a462e8a7459cde2180e4f54dcbfe9673f85d6bb51c8","target":"graph","created_at":"2026-07-17T00:20:53Z","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/2607.14144/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The Platonic Representation Hypothesis (PRH) holds that as models scale, representations of heterogeneous networks converge toward a shared model of reality. We propose its sequel and boundary, the Capability Convergence Hypothesis (CCH): under a fixed per-token inference budget, representational convergence does not entail capability convergence. Capability instead converges toward a class, the access-complete hybrid: any architecture holding both a compressive O(1)-state channel and a scalable verbatim-index channel. We anchor it on a witness task, the Newton's-apple problem in an infinite s","authors_text":"Chi Man Vong, Jianlin Chen, Wenhui Chen, Ziyao Lin","cross_cats":["cs.IT","math.IT"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.AI","submitted_at":"2026-07-14T05:52:12Z","title":"Capability from Access Structure, Not Scale: Lower Bounds and Pre-Registered Tests for Hybrid Sequence Models"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.14144","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":"sha256:8cba09630623abe7d1cbcf8575db5431d4f75c94313063cb6a6ebdc935ac05ae","target":"record","created_at":"2026-07-17T00:20:53Z","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":"9e595ab93ea1b3ccdf4a2112a0ac3e35f79e1f12c017c30896335c0c34dd0ffd","cross_cats_sorted":["cs.IT","math.IT"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.AI","submitted_at":"2026-07-14T05:52:12Z","title_canon_sha256":"fa2d2d960dee4fc9564aa2fe53de62ea645d0f58d3679ec0990bfc2919293a36"},"schema_version":"1.0","source":{"id":"2607.14144","kind":"arxiv","version":1}},"canonical_sha256":"eb40c7cf506dfbb5eccf2c95100ed0fcce64ab1dba87ed17dc886cb053c9bc2d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"eb40c7cf506dfbb5eccf2c95100ed0fcce64ab1dba87ed17dc886cb053c9bc2d","first_computed_at":"2026-07-17T00:20:53.847537Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-17T00:20:53.847537Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"8QDnwBXsbcEHTC4wVpz9sxR6S3if2UoByy1CbBObI/2f64Aw6nwIxrqsioZlyB7/PJM+vS67v28K0jSiRothDQ==","signature_status":"signed_v1","signed_at":"2026-07-17T00:20:53.848409Z","signed_message":"canonical_sha256_bytes"},"source_id":"2607.14144","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8cba09630623abe7d1cbcf8575db5431d4f75c94313063cb6a6ebdc935ac05ae","sha256:93f24fe9e99e3747eeef6a462e8a7459cde2180e4f54dcbfe9673f85d6bb51c8"],"state_sha256":"c034abc59fcca1d506b5f9844217a188ad874652bf90491fabd07924927ec8c2"}