{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:KRPIWLB5W3TUNG57DOOOBTPJ46","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":"f8bd50ec055c7b7c5ef958c7a742046703a980b277670faa9ce93c22fd8d3f83","cross_cats_sorted":["cs.CL","stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2026-07-10T15:04:02Z","title_canon_sha256":"1ef49a6e5d2e6b18c16bda570e6d4f89645b933695480c0bdccfdd46103fec96"},"schema_version":"1.0","source":{"id":"2607.09487","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.09487","created_at":"2026-07-13T01:20:13Z"},{"alias_kind":"arxiv_version","alias_value":"2607.09487v1","created_at":"2026-07-13T01:20:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.09487","created_at":"2026-07-13T01:20:13Z"},{"alias_kind":"pith_short_12","alias_value":"KRPIWLB5W3TU","created_at":"2026-07-13T01:20:13Z"},{"alias_kind":"pith_short_16","alias_value":"KRPIWLB5W3TUNG57","created_at":"2026-07-13T01:20:13Z"},{"alias_kind":"pith_short_8","alias_value":"KRPIWLB5","created_at":"2026-07-13T01:20:13Z"}],"graph_snapshots":[{"event_id":"sha256:be4da86547abd2b986a0602cc92c9e5a452c3a34614a3004eed80604a586e0a7","target":"graph","created_at":"2026-07-13T01:20:13Z","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/2607.09487/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Within-class variance in language-model representations is commonly read as incomplete neural collapse. We argue it is allocated information storage, and that the allocation obeys a law. A one-line centering identity voids a family of simplex equiangular-tight-frame claims, including our own earlier ones; in dimensionless variance shares across 14 models, macro-category structure carries only 4-12% of representational variance and within-token context carries 79-91%, stable across a 100x parameter range. On the theory side, token-level weight decay penalizes a category in proportion to its typ","authors_text":"Bruno Abrahao","cross_cats":["cs.CL","stat.ML"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2026-07-10T15:04:02Z","title":"Neural Collapse Is Forbidden: Information Floors in Language Models"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.09487","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":"sha256:856133a4ffa83fe25e5f6719a376bb428d2b155f20259acbdc8a457027479f7e","target":"record","created_at":"2026-07-13T01:20:13Z","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":"f8bd50ec055c7b7c5ef958c7a742046703a980b277670faa9ce93c22fd8d3f83","cross_cats_sorted":["cs.CL","stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2026-07-10T15:04:02Z","title_canon_sha256":"1ef49a6e5d2e6b18c16bda570e6d4f89645b933695480c0bdccfdd46103fec96"},"schema_version":"1.0","source":{"id":"2607.09487","kind":"arxiv","version":1}},"canonical_sha256":"545e8b2c3db6e7469bbf1b9ce0cde9e7b716fce2c7aca74274d945a0c7060e18","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"545e8b2c3db6e7469bbf1b9ce0cde9e7b716fce2c7aca74274d945a0c7060e18","first_computed_at":"2026-07-13T01:20:13.358105Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-13T01:20:13.358105Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Ql0qmYH5plXxdKJHjGVPeI8f5mdKqj/05UpYPs4tyc1noHXvAxcrnHh3oAc4F/3ap6NLZijP/C0nVN4EeX2VBA==","signature_status":"signed_v1","signed_at":"2026-07-13T01:20:13.359093Z","signed_message":"canonical_sha256_bytes"},"source_id":"2607.09487","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:856133a4ffa83fe25e5f6719a376bb428d2b155f20259acbdc8a457027479f7e","sha256:be4da86547abd2b986a0602cc92c9e5a452c3a34614a3004eed80604a586e0a7"],"state_sha256":"d525a4af8b34fd4865e931aa81e2dd42256f068847804676f983e2e7018989e5"}