{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:YH7NIUY7XIXZ3B6KEMNBAM57W3","short_pith_number":"pith:YH7NIUY7","canonical_record":{"source":{"id":"2607.03608","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2026-07-03T21:41:30Z","cross_cats_sorted":["cond-mat.stat-mech","math.IT","physics.soc-ph"],"title_canon_sha256":"de87807ec3c517b07c29a7b867e4be429997e322acabb5855e7f14bec71c793f","abstract_canon_sha256":"3a21a449c3712295b08bb9505c254e470a42b8e5a442332b033df6c1e7c6e7a5"},"schema_version":"1.0"},"canonical_sha256":"c1fed4531fba2f9d87ca231a1033bfb6f6796471ab86f341471b57ba921f6f87","source":{"kind":"arxiv","id":"2607.03608","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.03608","created_at":"2026-07-07T02:17:57Z"},{"alias_kind":"arxiv_version","alias_value":"2607.03608v1","created_at":"2026-07-07T02:17:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.03608","created_at":"2026-07-07T02:17:57Z"},{"alias_kind":"pith_short_12","alias_value":"YH7NIUY7XIXZ","created_at":"2026-07-07T02:17:57Z"},{"alias_kind":"pith_short_16","alias_value":"YH7NIUY7XIXZ3B6K","created_at":"2026-07-07T02:17:57Z"},{"alias_kind":"pith_short_8","alias_value":"YH7NIUY7","created_at":"2026-07-07T02:17:57Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:YH7NIUY7XIXZ3B6KEMNBAM57W3","target":"record","payload":{"canonical_record":{"source":{"id":"2607.03608","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2026-07-03T21:41:30Z","cross_cats_sorted":["cond-mat.stat-mech","math.IT","physics.soc-ph"],"title_canon_sha256":"de87807ec3c517b07c29a7b867e4be429997e322acabb5855e7f14bec71c793f","abstract_canon_sha256":"3a21a449c3712295b08bb9505c254e470a42b8e5a442332b033df6c1e7c6e7a5"},"schema_version":"1.0"},"canonical_sha256":"c1fed4531fba2f9d87ca231a1033bfb6f6796471ab86f341471b57ba921f6f87","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-07T02:17:57.262984Z","signature_b64":"cuu2NpkItVbQmJRQDGAgMmo7fD3Xz74kgBkiR4JyvmYHSl2z1O1gIFpr9zSkUwIvBh9+YJgf0R8km20pKOOkBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c1fed4531fba2f9d87ca231a1033bfb6f6796471ab86f341471b57ba921f6f87","last_reissued_at":"2026-07-07T02:17:57.262223Z","signature_status":"signed_v1","first_computed_at":"2026-07-07T02:17:57.262223Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2607.03608","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":"2026-07-07T02:17:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yfCHo6luBfkCBtIe+H189gn8dLdmg4LfSnDiRQEfc/KiRUGVqPOBumwj0jGk9ca6rmJjwcALElM+gnTX63xuDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T11:44:08.531891Z"},"content_sha256":"93a1a8f3c00cbb81ea681267c5917ca32aba80a356d435a400a0aa8d6bac0814","schema_version":"1.0","event_id":"sha256:93a1a8f3c00cbb81ea681267c5917ca32aba80a356d435a400a0aa8d6bac0814"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:YH7NIUY7XIXZ3B6KEMNBAM57W3","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Informational Cost of Structure: Representational Complexity in Networked Dynamical Systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech","math.IT","physics.soc-ph"],"primary_cat":"cs.IT","authors_text":"Cyril Rommens, Guilherme Ferraz de Arruda, Pietro Traversa, Yamir Moreno","submitted_at":"2026-07-03T21:41:30Z","abstract_excerpt":"How much information is required to represent a dynamical system in terms of an interaction structure and an evolution rule? We address this question using algorithmic information theory. We introduce Representational Complexity, the excess description length of a structure-plus-rule model relative to the shortest possible description of the dynamics itself. This intrinsic description defines a universal lower bound: no exact structural representation can be more concise. If arbitrary rules are allowed, graphs, hypergraphs, and other formalisms can all reach this bound by shifting information "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.03608","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/2607.03608/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":"2026-07-07T02:17:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xoj47QB5ThV4J1bq5Rxk33HN5UDtf9MwQ4gkwdEx5I/AnCnX6sGNoLWo+cbF5D7JDAHF6y5Ekle37nxjaas5BQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T11:44:08.532412Z"},"content_sha256":"27dfc749dc930b1d0db2b118e5c0b41f66897b666c8bcc812c3ae16021211285","schema_version":"1.0","event_id":"sha256:27dfc749dc930b1d0db2b118e5c0b41f66897b666c8bcc812c3ae16021211285"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/YH7NIUY7XIXZ3B6KEMNBAM57W3/bundle.json","state_url":"https://pith.science/pith/YH7NIUY7XIXZ3B6KEMNBAM57W3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/YH7NIUY7XIXZ3B6KEMNBAM57W3/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":"2026-08-09T11:44:08Z","links":{"resolver":"https://pith.science/pith/YH7NIUY7XIXZ3B6KEMNBAM57W3","bundle":"https://pith.science/pith/YH7NIUY7XIXZ3B6KEMNBAM57W3/bundle.json","state":"https://pith.science/pith/YH7NIUY7XIXZ3B6KEMNBAM57W3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/YH7NIUY7XIXZ3B6KEMNBAM57W3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:YH7NIUY7XIXZ3B6KEMNBAM57W3","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":"3a21a449c3712295b08bb9505c254e470a42b8e5a442332b033df6c1e7c6e7a5","cross_cats_sorted":["cond-mat.stat-mech","math.IT","physics.soc-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2026-07-03T21:41:30Z","title_canon_sha256":"de87807ec3c517b07c29a7b867e4be429997e322acabb5855e7f14bec71c793f"},"schema_version":"1.0","source":{"id":"2607.03608","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.03608","created_at":"2026-07-07T02:17:57Z"},{"alias_kind":"arxiv_version","alias_value":"2607.03608v1","created_at":"2026-07-07T02:17:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.03608","created_at":"2026-07-07T02:17:57Z"},{"alias_kind":"pith_short_12","alias_value":"YH7NIUY7XIXZ","created_at":"2026-07-07T02:17:57Z"},{"alias_kind":"pith_short_16","alias_value":"YH7NIUY7XIXZ3B6K","created_at":"2026-07-07T02:17:57Z"},{"alias_kind":"pith_short_8","alias_value":"YH7NIUY7","created_at":"2026-07-07T02:17:57Z"}],"graph_snapshots":[{"event_id":"sha256:27dfc749dc930b1d0db2b118e5c0b41f66897b666c8bcc812c3ae16021211285","target":"graph","created_at":"2026-07-07T02:17:57Z","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/2607.03608/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"How much information is required to represent a dynamical system in terms of an interaction structure and an evolution rule? We address this question using algorithmic information theory. We introduce Representational Complexity, the excess description length of a structure-plus-rule model relative to the shortest possible description of the dynamics itself. This intrinsic description defines a universal lower bound: no exact structural representation can be more concise. If arbitrary rules are allowed, graphs, hypergraphs, and other formalisms can all reach this bound by shifting information ","authors_text":"Cyril Rommens, Guilherme Ferraz de Arruda, Pietro Traversa, Yamir Moreno","cross_cats":["cond-mat.stat-mech","math.IT","physics.soc-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2026-07-03T21:41:30Z","title":"The Informational Cost of Structure: Representational Complexity in Networked Dynamical Systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.03608","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":"sha256:93a1a8f3c00cbb81ea681267c5917ca32aba80a356d435a400a0aa8d6bac0814","target":"record","created_at":"2026-07-07T02:17:57Z","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":"3a21a449c3712295b08bb9505c254e470a42b8e5a442332b033df6c1e7c6e7a5","cross_cats_sorted":["cond-mat.stat-mech","math.IT","physics.soc-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2026-07-03T21:41:30Z","title_canon_sha256":"de87807ec3c517b07c29a7b867e4be429997e322acabb5855e7f14bec71c793f"},"schema_version":"1.0","source":{"id":"2607.03608","kind":"arxiv","version":1}},"canonical_sha256":"c1fed4531fba2f9d87ca231a1033bfb6f6796471ab86f341471b57ba921f6f87","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c1fed4531fba2f9d87ca231a1033bfb6f6796471ab86f341471b57ba921f6f87","first_computed_at":"2026-07-07T02:17:57.262223Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-07T02:17:57.262223Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"cuu2NpkItVbQmJRQDGAgMmo7fD3Xz74kgBkiR4JyvmYHSl2z1O1gIFpr9zSkUwIvBh9+YJgf0R8km20pKOOkBA==","signature_status":"signed_v1","signed_at":"2026-07-07T02:17:57.262984Z","signed_message":"canonical_sha256_bytes"},"source_id":"2607.03608","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:93a1a8f3c00cbb81ea681267c5917ca32aba80a356d435a400a0aa8d6bac0814","sha256:27dfc749dc930b1d0db2b118e5c0b41f66897b666c8bcc812c3ae16021211285"],"state_sha256":"83b78368ff706cea51bdc61b1a7285a76e8af7903a83c114d7f7e9ee30d09ba3"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rhJKYCsULnnUCSf9XmBpObgHQ4DccLYDKzhQ+KSlq4pLxhyPnsHKuPeEhxsgRnt/BWKs+/YWe1kLIQ0PyNplDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-09T11:44:08.538499Z","bundle_sha256":"30ef9dcee5a29db8d8c7b44c2cfa3e2fbfcc5519aa184ca3486a81873311bf22"}}