{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:E55V4LH3KIEDGVMAOZOVCO5C2F","short_pith_number":"pith:E55V4LH3","canonical_record":{"source":{"id":"2606.29679","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"cs.LG","submitted_at":"2026-06-29T00:57:57Z","cross_cats_sorted":[],"title_canon_sha256":"42e2ec0e7b4bd659c68dee7d3822de0e0d926ee51b276fa4ed3d0e1e7ba9b6c4","abstract_canon_sha256":"2be14948b4e1f20f16484dd127217b5454f8fb7c2c4252be775735070eba057f"},"schema_version":"1.0"},"canonical_sha256":"277b5e2cfb5208335580765d513ba2d1631a0a98112a3fb1f31c08dc619daea0","source":{"kind":"arxiv","id":"2606.29679","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.29679","created_at":"2026-06-30T02:17:30Z"},{"alias_kind":"arxiv_version","alias_value":"2606.29679v1","created_at":"2026-06-30T02:17:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.29679","created_at":"2026-06-30T02:17:30Z"},{"alias_kind":"pith_short_12","alias_value":"E55V4LH3KIED","created_at":"2026-06-30T02:17:30Z"},{"alias_kind":"pith_short_16","alias_value":"E55V4LH3KIEDGVMA","created_at":"2026-06-30T02:17:30Z"},{"alias_kind":"pith_short_8","alias_value":"E55V4LH3","created_at":"2026-06-30T02:17:30Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:E55V4LH3KIEDGVMAOZOVCO5C2F","target":"record","payload":{"canonical_record":{"source":{"id":"2606.29679","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"cs.LG","submitted_at":"2026-06-29T00:57:57Z","cross_cats_sorted":[],"title_canon_sha256":"42e2ec0e7b4bd659c68dee7d3822de0e0d926ee51b276fa4ed3d0e1e7ba9b6c4","abstract_canon_sha256":"2be14948b4e1f20f16484dd127217b5454f8fb7c2c4252be775735070eba057f"},"schema_version":"1.0"},"canonical_sha256":"277b5e2cfb5208335580765d513ba2d1631a0a98112a3fb1f31c08dc619daea0","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-30T02:17:30.407831Z","signature_b64":"n0A12tQp6Y5wjgt1YntfI7OhFsYUUO3SmXKkv2CN9gCAYZofEzpfTdVXOfkVfC8WX2g7Aa7yPvCH3RjrQaX3Aw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"277b5e2cfb5208335580765d513ba2d1631a0a98112a3fb1f31c08dc619daea0","last_reissued_at":"2026-06-30T02:17:30.407327Z","signature_status":"signed_v1","first_computed_at":"2026-06-30T02:17:30.407327Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2606.29679","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-06-30T02:17:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qqVAturxoymubt4XbIfxHmgGyiel38oDf8N2GXzV2tKW1k/3hkxwfxwPs8B/sq7rcWBG46XIGjzWF3owZ4alDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-30T11:05:08.218980Z"},"content_sha256":"05f1cd5c261377a2601a1d18f3eb6c09da6225954866dec14e4eed0cdcc24f31","schema_version":"1.0","event_id":"sha256:05f1cd5c261377a2601a1d18f3eb6c09da6225954866dec14e4eed0cdcc24f31"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:E55V4LH3KIEDGVMAOZOVCO5C2F","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Learning as Observable Matrix Dynamics: Diffusive Relaxations versus Phase Transitions","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":[],"primary_cat":"cs.LG","authors_text":"Igor Halperin","submitted_at":"2026-06-29T00:57:57Z","abstract_excerpt":"Observable Matrix Dynamics (OMD) is a diagnostic framework that probes the dynamics of high-dimensional internal representations of inputs by a neural network via a fixed-size $N \\times N$ distance matrix $M(t)$ on a held set of $N$ inputs. OMD uses methods of random matrix theory and particle dynamics to explore spectral reorganisations that are missed by scalar loss functions, but are informative of the training process. We read $M(t)$ against a perturbative ambient-versus-latent decomposition extending the Bogomolny--Bohigas--Schmit (BBS) theory of random distance matrices, with per-snapsho"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.29679","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.29679/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-06-30T02:17:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rGSFm0vCsufbaJ/xHDNArSjL7xBRXc9NtQpNc0EneTctT/HXf5RwcsS0xa1+dxuIAAMkZI8cHcEWWUS6NFIsBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-30T11:05:08.219358Z"},"content_sha256":"7817e323ed343a5320e399d0827d6b53335fc1299306436968b117bf0cd95d52","schema_version":"1.0","event_id":"sha256:7817e323ed343a5320e399d0827d6b53335fc1299306436968b117bf0cd95d52"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/E55V4LH3KIEDGVMAOZOVCO5C2F/bundle.json","state_url":"https://pith.science/pith/E55V4LH3KIEDGVMAOZOVCO5C2F/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/E55V4LH3KIEDGVMAOZOVCO5C2F/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-30T11:05:08Z","links":{"resolver":"https://pith.science/pith/E55V4LH3KIEDGVMAOZOVCO5C2F","bundle":"https://pith.science/pith/E55V4LH3KIEDGVMAOZOVCO5C2F/bundle.json","state":"https://pith.science/pith/E55V4LH3KIEDGVMAOZOVCO5C2F/state.json","well_known_bundle":"https://pith.science/.well-known/pith/E55V4LH3KIEDGVMAOZOVCO5C2F/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:E55V4LH3KIEDGVMAOZOVCO5C2F","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":"2be14948b4e1f20f16484dd127217b5454f8fb7c2c4252be775735070eba057f","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"cs.LG","submitted_at":"2026-06-29T00:57:57Z","title_canon_sha256":"42e2ec0e7b4bd659c68dee7d3822de0e0d926ee51b276fa4ed3d0e1e7ba9b6c4"},"schema_version":"1.0","source":{"id":"2606.29679","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.29679","created_at":"2026-06-30T02:17:30Z"},{"alias_kind":"arxiv_version","alias_value":"2606.29679v1","created_at":"2026-06-30T02:17:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.29679","created_at":"2026-06-30T02:17:30Z"},{"alias_kind":"pith_short_12","alias_value":"E55V4LH3KIED","created_at":"2026-06-30T02:17:30Z"},{"alias_kind":"pith_short_16","alias_value":"E55V4LH3KIEDGVMA","created_at":"2026-06-30T02:17:30Z"},{"alias_kind":"pith_short_8","alias_value":"E55V4LH3","created_at":"2026-06-30T02:17:30Z"}],"graph_snapshots":[{"event_id":"sha256:7817e323ed343a5320e399d0827d6b53335fc1299306436968b117bf0cd95d52","target":"graph","created_at":"2026-06-30T02:17:30Z","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/2606.29679/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Observable Matrix Dynamics (OMD) is a diagnostic framework that probes the dynamics of high-dimensional internal representations of inputs by a neural network via a fixed-size $N \\times N$ distance matrix $M(t)$ on a held set of $N$ inputs. OMD uses methods of random matrix theory and particle dynamics to explore spectral reorganisations that are missed by scalar loss functions, but are informative of the training process. We read $M(t)$ against a perturbative ambient-versus-latent decomposition extending the Bogomolny--Bohigas--Schmit (BBS) theory of random distance matrices, with per-snapsho","authors_text":"Igor Halperin","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"cs.LG","submitted_at":"2026-06-29T00:57:57Z","title":"Learning as Observable Matrix Dynamics: Diffusive Relaxations versus Phase Transitions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.29679","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":"sha256:05f1cd5c261377a2601a1d18f3eb6c09da6225954866dec14e4eed0cdcc24f31","target":"record","created_at":"2026-06-30T02:17:30Z","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":"2be14948b4e1f20f16484dd127217b5454f8fb7c2c4252be775735070eba057f","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"cs.LG","submitted_at":"2026-06-29T00:57:57Z","title_canon_sha256":"42e2ec0e7b4bd659c68dee7d3822de0e0d926ee51b276fa4ed3d0e1e7ba9b6c4"},"schema_version":"1.0","source":{"id":"2606.29679","kind":"arxiv","version":1}},"canonical_sha256":"277b5e2cfb5208335580765d513ba2d1631a0a98112a3fb1f31c08dc619daea0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"277b5e2cfb5208335580765d513ba2d1631a0a98112a3fb1f31c08dc619daea0","first_computed_at":"2026-06-30T02:17:30.407327Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-30T02:17:30.407327Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"n0A12tQp6Y5wjgt1YntfI7OhFsYUUO3SmXKkv2CN9gCAYZofEzpfTdVXOfkVfC8WX2g7Aa7yPvCH3RjrQaX3Aw==","signature_status":"signed_v1","signed_at":"2026-06-30T02:17:30.407831Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.29679","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:05f1cd5c261377a2601a1d18f3eb6c09da6225954866dec14e4eed0cdcc24f31","sha256:7817e323ed343a5320e399d0827d6b53335fc1299306436968b117bf0cd95d52"],"state_sha256":"31b565620b56d732bc6afb856bea831b8bba65d0cee6f3ffe1933d04294735e8"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0Yijbk1glpH5T1KFUPQEnOCDuIs5d+jp0ZL7eXvaSZxO12qoWroNT7Nppvj4o6+uielxBkCe+Cr3eESlwDHFAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-30T11:05:08.221535Z","bundle_sha256":"0587d11580864a3a50ff83030d9a1eda8777af7b73592070ccf9a003107b9b96"}}