{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:TPH5DNGRKANB572D2U56EMWJNV","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":"91f3b2e2355b89c7a76d6d91499bf381907c70fb3f47ba5ea6bc7884bb50c0e5","cross_cats_sorted":["math-ph","math.MP"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"nlin.CD","submitted_at":"2026-05-31T19:48:39Z","title_canon_sha256":"1a52f92be3e7c221958c2ed58c548fbd9660d30bd66deb0364333fecd043d437"},"schema_version":"1.0","source":{"id":"2606.02649","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.02649","created_at":"2026-06-03T00:05:05Z"},{"alias_kind":"arxiv_version","alias_value":"2606.02649v1","created_at":"2026-06-03T00:05:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.02649","created_at":"2026-06-03T00:05:05Z"},{"alias_kind":"pith_short_12","alias_value":"TPH5DNGRKANB","created_at":"2026-06-03T00:05:05Z"},{"alias_kind":"pith_short_16","alias_value":"TPH5DNGRKANB572D","created_at":"2026-06-03T00:05:05Z"},{"alias_kind":"pith_short_8","alias_value":"TPH5DNGR","created_at":"2026-06-03T00:05:05Z"}],"graph_snapshots":[{"event_id":"sha256:8b006d0c540dfc62e9c37c5374225faf46c1d31adc6cb0eac4bb4fe0df7d4912","target":"graph","created_at":"2026-06-03T00:05:05Z","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/2606.02649/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We introduce temporal matrix scale invariance (tMSI), a mathematical structure for the two-time correlation kernel of a multivariate observable. A kernel $C(t,t')$ satisfies tMSI of order $\\alpha$ if $C(kt, kt') = k^{-\\alpha}C(t,t')$ for all $k>0$; this condition holds near a tipping point, where the divergence of the coherence time produces temporal scale freedom. By a kernel factorization theorem, every tMSI kernel separates into a power-law envelope $(tt')^{-\\alpha/2}$ and a shape function $F(t/t')$ diagonalized by the Mellin transform. This reveals a decoupling of two independent exponents","authors_text":"Alejandro Frank, Laurence A. Jacobs","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"nlin.CD","submitted_at":"2026-05-31T19:48:39Z","title":"Temporal Matrix Scale Invariance and the Classification of Tipping Points"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.02649","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:c32fb97bc0e5b8b8181580489847d07da83d40bdc49f6d86b5ca349699e3cc14","target":"record","created_at":"2026-06-03T00:05:05Z","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":"91f3b2e2355b89c7a76d6d91499bf381907c70fb3f47ba5ea6bc7884bb50c0e5","cross_cats_sorted":["math-ph","math.MP"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"nlin.CD","submitted_at":"2026-05-31T19:48:39Z","title_canon_sha256":"1a52f92be3e7c221958c2ed58c548fbd9660d30bd66deb0364333fecd043d437"},"schema_version":"1.0","source":{"id":"2606.02649","kind":"arxiv","version":1}},"canonical_sha256":"9bcfd1b4d1501a1eff43d53be232c96d7ad8534fa5021fbae4f9c925e36da827","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9bcfd1b4d1501a1eff43d53be232c96d7ad8534fa5021fbae4f9c925e36da827","first_computed_at":"2026-06-03T00:05:05.592152Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-03T00:05:05.592152Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"RaazstZ2itr9JDeCFCi7MMF0hlYmUpbPRR2Rg0n+0dt6rpf6ODwiAuYH12W4LpMM36CAFvqO4BDmjchQ45KJBg==","signature_status":"signed_v1","signed_at":"2026-06-03T00:05:05.592575Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.02649","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c32fb97bc0e5b8b8181580489847d07da83d40bdc49f6d86b5ca349699e3cc14","sha256:8b006d0c540dfc62e9c37c5374225faf46c1d31adc6cb0eac4bb4fe0df7d4912"],"state_sha256":"c479e01f6656c3077a56ce08bf0cd80de79a12a066d160f08f99695207f77713"}