{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2021:VJJ36ZD3VNMDW6T27FRBKGIGPM","short_pith_number":"pith:VJJ36ZD3","canonical_record":{"source":{"id":"2105.12735","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2021-05-26T18:00:00Z","cross_cats_sorted":["gr-qc"],"title_canon_sha256":"0d750f4f8906cafc89a5cfa6be46cebb807a97a6fcd0e9c185d6a2152aa75be7","abstract_canon_sha256":"312a2bd0b3fdf96e2caf6d6abc2cd037e6d4b55946bedb3df49ec5418741551a"},"schema_version":"1.0"},"canonical_sha256":"aa53bf647bab583b7a7af9621519067b2e0bc20edaf615a05745b2e678cc55ef","source":{"kind":"arxiv","id":"2105.12735","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2105.12735","created_at":"2026-07-05T03:44:53Z"},{"alias_kind":"arxiv_version","alias_value":"2105.12735v3","created_at":"2026-07-05T03:44:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2105.12735","created_at":"2026-07-05T03:44:53Z"},{"alias_kind":"pith_short_12","alias_value":"VJJ36ZD3VNMD","created_at":"2026-07-05T03:44:53Z"},{"alias_kind":"pith_short_16","alias_value":"VJJ36ZD3VNMDW6T2","created_at":"2026-07-05T03:44:53Z"},{"alias_kind":"pith_short_8","alias_value":"VJJ36ZD3","created_at":"2026-07-05T03:44:53Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2021:VJJ36ZD3VNMDW6T27FRBKGIGPM","target":"record","payload":{"canonical_record":{"source":{"id":"2105.12735","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2021-05-26T18:00:00Z","cross_cats_sorted":["gr-qc"],"title_canon_sha256":"0d750f4f8906cafc89a5cfa6be46cebb807a97a6fcd0e9c185d6a2152aa75be7","abstract_canon_sha256":"312a2bd0b3fdf96e2caf6d6abc2cd037e6d4b55946bedb3df49ec5418741551a"},"schema_version":"1.0"},"canonical_sha256":"aa53bf647bab583b7a7af9621519067b2e0bc20edaf615a05745b2e678cc55ef","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T03:44:53.805155Z","signature_b64":"NUiY/tDJx6M4kjgvQFeDUnjJCNBrT7dvomAPbQ3F0vn8ScPjQbbIQ6Oz2CqrA6Mi0Hnq/anjUsKIEm5WOWlCAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"aa53bf647bab583b7a7af9621519067b2e0bc20edaf615a05745b2e678cc55ef","last_reissued_at":"2026-07-05T03:44:53.804688Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T03:44:53.804688Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2105.12735","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T03:44:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HP/WPL77v5i1tNQamsgJonTz6qbHAr2UbhhqCiXt5KoJ9aPrv+6hOkYzZk+CqolxKbMRdvT0EeM5kOY+l4NSBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-05T17:26:57.123620Z"},"content_sha256":"ee4a6d33a787bf06bfc8f2edd989b964bc5f0830f5d9316de8b456ea86e5b3f2","schema_version":"1.0","event_id":"sha256:ee4a6d33a787bf06bfc8f2edd989b964bc5f0830f5d9316de8b456ea86e5b3f2"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2021:VJJ36ZD3VNMDW6T27FRBKGIGPM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Lorentzian threads as 'gatelines' and holographic complexity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["gr-qc"],"primary_cat":"hep-th","authors_text":"Andrea Russo, Andrew Svesko, Juan F. Pedraza, Zachary Weller-Davies","submitted_at":"2021-05-26T18:00:00Z","abstract_excerpt":"The continuous min flow-max cut principle is used to reformulate the 'complexity=volume' conjecture using Lorentzian flows -- divergenceless norm-bounded timelike vector fields whose minimum flux through a boundary subregion is equal to the volume of the homologous maximal bulk Cauchy slice. The nesting property is used to show the rate of complexity is bounded below by \"conditional complexity\", describing a multi-step optimization with intermediate and final target states. Conceptually, discretized Lorentzian flows are interpreted in terms of threads or gatelines such that complexity is equal"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2105.12735","kind":"arxiv","version":3},"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/2105.12735/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":"2026-07-05T03:44:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Jxqj69W/EThXXf7NKP2JOqfFKcGT/r0/AG1dq/3yofRu3ASMpHcYQnM3JasWBIW/DlYeACovdIH51Q0UQVKlCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-05T17:26:57.124617Z"},"content_sha256":"f491005b063b27df09a74130bb9cd8e69c5ca6d8dcb0319cf0f7179f033cc2d8","schema_version":"1.0","event_id":"sha256:f491005b063b27df09a74130bb9cd8e69c5ca6d8dcb0319cf0f7179f033cc2d8"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VJJ36ZD3VNMDW6T27FRBKGIGPM/bundle.json","state_url":"https://pith.science/pith/VJJ36ZD3VNMDW6T27FRBKGIGPM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VJJ36ZD3VNMDW6T27FRBKGIGPM/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":"2026-08-05T17:26:57Z","links":{"resolver":"https://pith.science/pith/VJJ36ZD3VNMDW6T27FRBKGIGPM","bundle":"https://pith.science/pith/VJJ36ZD3VNMDW6T27FRBKGIGPM/bundle.json","state":"https://pith.science/pith/VJJ36ZD3VNMDW6T27FRBKGIGPM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VJJ36ZD3VNMDW6T27FRBKGIGPM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:VJJ36ZD3VNMDW6T27FRBKGIGPM","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":"312a2bd0b3fdf96e2caf6d6abc2cd037e6d4b55946bedb3df49ec5418741551a","cross_cats_sorted":["gr-qc"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2021-05-26T18:00:00Z","title_canon_sha256":"0d750f4f8906cafc89a5cfa6be46cebb807a97a6fcd0e9c185d6a2152aa75be7"},"schema_version":"1.0","source":{"id":"2105.12735","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2105.12735","created_at":"2026-07-05T03:44:53Z"},{"alias_kind":"arxiv_version","alias_value":"2105.12735v3","created_at":"2026-07-05T03:44:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2105.12735","created_at":"2026-07-05T03:44:53Z"},{"alias_kind":"pith_short_12","alias_value":"VJJ36ZD3VNMD","created_at":"2026-07-05T03:44:53Z"},{"alias_kind":"pith_short_16","alias_value":"VJJ36ZD3VNMDW6T2","created_at":"2026-07-05T03:44:53Z"},{"alias_kind":"pith_short_8","alias_value":"VJJ36ZD3","created_at":"2026-07-05T03:44:53Z"}],"graph_snapshots":[{"event_id":"sha256:f491005b063b27df09a74130bb9cd8e69c5ca6d8dcb0319cf0f7179f033cc2d8","target":"graph","created_at":"2026-07-05T03:44:53Z","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/2105.12735/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The continuous min flow-max cut principle is used to reformulate the 'complexity=volume' conjecture using Lorentzian flows -- divergenceless norm-bounded timelike vector fields whose minimum flux through a boundary subregion is equal to the volume of the homologous maximal bulk Cauchy slice. The nesting property is used to show the rate of complexity is bounded below by \"conditional complexity\", describing a multi-step optimization with intermediate and final target states. Conceptually, discretized Lorentzian flows are interpreted in terms of threads or gatelines such that complexity is equal","authors_text":"Andrea Russo, Andrew Svesko, Juan F. Pedraza, Zachary Weller-Davies","cross_cats":["gr-qc"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2021-05-26T18:00:00Z","title":"Lorentzian threads as 'gatelines' and holographic complexity"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2105.12735","kind":"arxiv","version":3},"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:ee4a6d33a787bf06bfc8f2edd989b964bc5f0830f5d9316de8b456ea86e5b3f2","target":"record","created_at":"2026-07-05T03:44:53Z","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":"312a2bd0b3fdf96e2caf6d6abc2cd037e6d4b55946bedb3df49ec5418741551a","cross_cats_sorted":["gr-qc"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2021-05-26T18:00:00Z","title_canon_sha256":"0d750f4f8906cafc89a5cfa6be46cebb807a97a6fcd0e9c185d6a2152aa75be7"},"schema_version":"1.0","source":{"id":"2105.12735","kind":"arxiv","version":3}},"canonical_sha256":"aa53bf647bab583b7a7af9621519067b2e0bc20edaf615a05745b2e678cc55ef","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"aa53bf647bab583b7a7af9621519067b2e0bc20edaf615a05745b2e678cc55ef","first_computed_at":"2026-07-05T03:44:53.804688Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T03:44:53.804688Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"NUiY/tDJx6M4kjgvQFeDUnjJCNBrT7dvomAPbQ3F0vn8ScPjQbbIQ6Oz2CqrA6Mi0Hnq/anjUsKIEm5WOWlCAw==","signature_status":"signed_v1","signed_at":"2026-07-05T03:44:53.805155Z","signed_message":"canonical_sha256_bytes"},"source_id":"2105.12735","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ee4a6d33a787bf06bfc8f2edd989b964bc5f0830f5d9316de8b456ea86e5b3f2","sha256:f491005b063b27df09a74130bb9cd8e69c5ca6d8dcb0319cf0f7179f033cc2d8"],"state_sha256":"af64ae26f0be66321f5af4b6f94dfdea58ab6069e718ef41436bbb8dc24d17d9"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+52HQvqNNgriVl04CbIyxxIAKJafgjzBI9FHU5SMzX9FZqEoRL7i9/eof9Ogb2iK1a8nYa876cfGnZyzFqpiBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-05T17:26:57.131665Z","bundle_sha256":"e8b6a964e426ebf4248466ee36e1bea65cfb466814f4130f71e3ef0bbb1d719a"}}