{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:YEQNNNUGWGHRH5BANURR45HVCX","short_pith_number":"pith:YEQNNNUG","canonical_record":{"source":{"id":"2606.22895","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2026-06-22T06:11:46Z","cross_cats_sorted":[],"title_canon_sha256":"ba5be41b3daa4afec960ea3de17528d28696d4fe6b7f95c4268d611bd00d997b","abstract_canon_sha256":"ef7e31dedc2f8595f93e77849c65deab91de052136608688eaa465c725597573"},"schema_version":"1.0"},"canonical_sha256":"c120d6b686b18f13f4206d231e74f515f5f60588324e7bfe75affa61d816720f","source":{"kind":"arxiv","id":"2606.22895","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.22895","created_at":"2026-06-23T03:14:03Z"},{"alias_kind":"arxiv_version","alias_value":"2606.22895v1","created_at":"2026-06-23T03:14:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.22895","created_at":"2026-06-23T03:14:03Z"},{"alias_kind":"pith_short_12","alias_value":"YEQNNNUGWGHR","created_at":"2026-06-23T03:14:03Z"},{"alias_kind":"pith_short_16","alias_value":"YEQNNNUGWGHRH5BA","created_at":"2026-06-23T03:14:03Z"},{"alias_kind":"pith_short_8","alias_value":"YEQNNNUG","created_at":"2026-06-23T03:14:03Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:YEQNNNUGWGHRH5BANURR45HVCX","target":"record","payload":{"canonical_record":{"source":{"id":"2606.22895","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2026-06-22T06:11:46Z","cross_cats_sorted":[],"title_canon_sha256":"ba5be41b3daa4afec960ea3de17528d28696d4fe6b7f95c4268d611bd00d997b","abstract_canon_sha256":"ef7e31dedc2f8595f93e77849c65deab91de052136608688eaa465c725597573"},"schema_version":"1.0"},"canonical_sha256":"c120d6b686b18f13f4206d231e74f515f5f60588324e7bfe75affa61d816720f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-23T03:14:03.516258Z","signature_b64":"iUqvqYpFtNcmQZezoNEslEfFynXZOPA6+IHC0otuaWrBClzHWuPpZe0FEduunO7SC65MgS3SPY7v9SlI7wFYBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c120d6b686b18f13f4206d231e74f515f5f60588324e7bfe75affa61d816720f","last_reissued_at":"2026-06-23T03:14:03.515873Z","signature_status":"signed_v1","first_computed_at":"2026-06-23T03:14:03.515873Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2606.22895","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":"2026-06-23T03:14:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"y1bKymQu3HsAca8lo+TkF2x+gWqNKT5Nds58MnhF9Tp0i35r1SACOamEuIQO/x/aw5UuhvSHQdRMnsZgCyPzDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-03T20:48:37.518214Z"},"content_sha256":"a1087aa3fbef735b2ec582370c42313943fdd6a3ad6c40edb59ab09a6e3b62c5","schema_version":"1.0","event_id":"sha256:a1087aa3fbef735b2ec582370c42313943fdd6a3ad6c40edb59ab09a6e3b62c5"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:YEQNNNUGWGHRH5BANURR45HVCX","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Learning Graphs through Continuous Information Entropy Fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.LG","authors_text":"Bo Sun, Hui Cong, Yisheng An, Ziheng Jiao","submitted_at":"2026-06-22T06:11:46Z","abstract_excerpt":"Graph theory is inherently descriptive, capturing what relationships exist but not why they arise, because it treats edges as primitive constructs. This paper proposes a new explanatory framework for graph learning, where relationships emerge from latent continuous information entropy fields, and a graph becomes a discrete instantiation of an underlying field. To formalize this field, we introduce the Field-informed Graph Network (FGN). It learns a scalar field from node features and leverages it to modulate message passing. The information-theoretic objective balances structural fidelity with"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.22895","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/2606.22895/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":"2026-06-23T03:14:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7lMvdVbLioAk6iTTmHqwmcvXPU3IQDflwSucaOJjNaOIPdnZ/ApmuxBfNQ/NMOsA5DN4wN8+GkZxnMwqs5qgCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-03T20:48:37.518720Z"},"content_sha256":"d31749132655692c3204faa811bbe7b037be6f77abc701e83f506f2c7adc15f0","schema_version":"1.0","event_id":"sha256:d31749132655692c3204faa811bbe7b037be6f77abc701e83f506f2c7adc15f0"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/YEQNNNUGWGHRH5BANURR45HVCX/bundle.json","state_url":"https://pith.science/pith/YEQNNNUGWGHRH5BANURR45HVCX/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/YEQNNNUGWGHRH5BANURR45HVCX/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":"2026-08-03T20:48:37Z","links":{"resolver":"https://pith.science/pith/YEQNNNUGWGHRH5BANURR45HVCX","bundle":"https://pith.science/pith/YEQNNNUGWGHRH5BANURR45HVCX/bundle.json","state":"https://pith.science/pith/YEQNNNUGWGHRH5BANURR45HVCX/state.json","well_known_bundle":"https://pith.science/.well-known/pith/YEQNNNUGWGHRH5BANURR45HVCX/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:YEQNNNUGWGHRH5BANURR45HVCX","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":"ef7e31dedc2f8595f93e77849c65deab91de052136608688eaa465c725597573","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2026-06-22T06:11:46Z","title_canon_sha256":"ba5be41b3daa4afec960ea3de17528d28696d4fe6b7f95c4268d611bd00d997b"},"schema_version":"1.0","source":{"id":"2606.22895","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.22895","created_at":"2026-06-23T03:14:03Z"},{"alias_kind":"arxiv_version","alias_value":"2606.22895v1","created_at":"2026-06-23T03:14:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.22895","created_at":"2026-06-23T03:14:03Z"},{"alias_kind":"pith_short_12","alias_value":"YEQNNNUGWGHR","created_at":"2026-06-23T03:14:03Z"},{"alias_kind":"pith_short_16","alias_value":"YEQNNNUGWGHRH5BA","created_at":"2026-06-23T03:14:03Z"},{"alias_kind":"pith_short_8","alias_value":"YEQNNNUG","created_at":"2026-06-23T03:14:03Z"}],"graph_snapshots":[{"event_id":"sha256:d31749132655692c3204faa811bbe7b037be6f77abc701e83f506f2c7adc15f0","target":"graph","created_at":"2026-06-23T03:14:03Z","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/2606.22895/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Graph theory is inherently descriptive, capturing what relationships exist but not why they arise, because it treats edges as primitive constructs. This paper proposes a new explanatory framework for graph learning, where relationships emerge from latent continuous information entropy fields, and a graph becomes a discrete instantiation of an underlying field. To formalize this field, we introduce the Field-informed Graph Network (FGN). It learns a scalar field from node features and leverages it to modulate message passing. The information-theoretic objective balances structural fidelity with","authors_text":"Bo Sun, Hui Cong, Yisheng An, Ziheng Jiao","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2026-06-22T06:11:46Z","title":"Learning Graphs through Continuous Information Entropy Fields"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.22895","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:a1087aa3fbef735b2ec582370c42313943fdd6a3ad6c40edb59ab09a6e3b62c5","target":"record","created_at":"2026-06-23T03:14:03Z","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":"ef7e31dedc2f8595f93e77849c65deab91de052136608688eaa465c725597573","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2026-06-22T06:11:46Z","title_canon_sha256":"ba5be41b3daa4afec960ea3de17528d28696d4fe6b7f95c4268d611bd00d997b"},"schema_version":"1.0","source":{"id":"2606.22895","kind":"arxiv","version":1}},"canonical_sha256":"c120d6b686b18f13f4206d231e74f515f5f60588324e7bfe75affa61d816720f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c120d6b686b18f13f4206d231e74f515f5f60588324e7bfe75affa61d816720f","first_computed_at":"2026-06-23T03:14:03.515873Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-23T03:14:03.515873Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"iUqvqYpFtNcmQZezoNEslEfFynXZOPA6+IHC0otuaWrBClzHWuPpZe0FEduunO7SC65MgS3SPY7v9SlI7wFYBA==","signature_status":"signed_v1","signed_at":"2026-06-23T03:14:03.516258Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.22895","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a1087aa3fbef735b2ec582370c42313943fdd6a3ad6c40edb59ab09a6e3b62c5","sha256:d31749132655692c3204faa811bbe7b037be6f77abc701e83f506f2c7adc15f0"],"state_sha256":"c5d34f983999559f4cc477507e0e7e6571d11b63af7c8b22efd4a851db577cb2"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vhp9In1oiRoyE2CpKtKdRb09x6OQ5Heyd8SjCdsLTuWqUvr6iwDtxqlrgygFtGGrnpwgM9dyc8M56EkG1Md2CQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-03T20:48:37.522593Z","bundle_sha256":"6096df089a4cdfa391ab704bd6971bc935ff8a76b0d85277fbea065a8608ed0f"}}