{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:DBUVE4BAXRNAAICRE3QO5BRBY2","short_pith_number":"pith:DBUVE4BA","canonical_record":{"source":{"id":"1012.1332","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2010-12-03T09:41:17Z","cross_cats_sorted":["cs.FL","nlin.CG"],"title_canon_sha256":"398f7a472f5e2af1f632a9a31ad74b886127d23f9ed2f22958da95953595a483","abstract_canon_sha256":"36f8a6af3a28194aaa1f9e33f45877017b69f136b0bb553425888f49fda586e6"},"schema_version":"1.0"},"canonical_sha256":"1869527020bc5a00205126e0ee8621c6a4f2463ad5f36061e82303ccc8809cac","source":{"kind":"arxiv","id":"1012.1332","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1012.1332","created_at":"2026-05-18T04:34:01Z"},{"alias_kind":"arxiv_version","alias_value":"1012.1332v1","created_at":"2026-05-18T04:34:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1012.1332","created_at":"2026-05-18T04:34:01Z"},{"alias_kind":"pith_short_12","alias_value":"DBUVE4BAXRNA","created_at":"2026-05-18T12:26:06Z"},{"alias_kind":"pith_short_16","alias_value":"DBUVE4BAXRNAAICR","created_at":"2026-05-18T12:26:06Z"},{"alias_kind":"pith_short_8","alias_value":"DBUVE4BA","created_at":"2026-05-18T12:26:06Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:DBUVE4BAXRNAAICRE3QO5BRBY2","target":"record","payload":{"canonical_record":{"source":{"id":"1012.1332","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2010-12-03T09:41:17Z","cross_cats_sorted":["cs.FL","nlin.CG"],"title_canon_sha256":"398f7a472f5e2af1f632a9a31ad74b886127d23f9ed2f22958da95953595a483","abstract_canon_sha256":"36f8a6af3a28194aaa1f9e33f45877017b69f136b0bb553425888f49fda586e6"},"schema_version":"1.0"},"canonical_sha256":"1869527020bc5a00205126e0ee8621c6a4f2463ad5f36061e82303ccc8809cac","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:34:01.177050Z","signature_b64":"8HgK0eamNsrd47X/wNI+1KIfdtPUrimphJgiqDI8m8rUL4SDBjW51M5x6dcIoauEaaBOwtUD3ZtiL6/dkwX3CA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1869527020bc5a00205126e0ee8621c6a4f2463ad5f36061e82303ccc8809cac","last_reissued_at":"2026-05-18T04:34:01.176671Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:34:01.176671Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1012.1332","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":"2026-05-18T04:34:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XIVOx8rdNodv217/X1xV6izcQcEA/Pl5aeSasYrGCGSclHgXWmSU6yFNW7VCC9s3iKdwFrFi6ohXGp7hnARtBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T04:16:46.673338Z"},"content_sha256":"001c3a5327173ca672013449561ea8660f37cb77130686e60a40d36427c22272","schema_version":"1.0","event_id":"sha256:001c3a5327173ca672013449561ea8660f37cb77130686e60a40d36427c22272"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:DBUVE4BAXRNAAICRE3QO5BRBY2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Time-Symmetric Cellular Automata","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.FL","nlin.CG"],"primary_cat":"cs.DM","authors_text":"Anahi Gajardo, Andr\\'es Moreira","submitted_at":"2010-12-03T09:41:17Z","abstract_excerpt":"Together with the concept of reversibility, another relevant physical notion is time-symmetry, which expresses that there is no way of distinguishing between backward and forward time directions. This notion, found in physical theories, has been neglected in the area of discrete dynamical systems. Here we formalize it in the context of cellular automata and establish some basic facts and relations. We also state some open problems that may encourage further research on the topic."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1012.1332","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":""},"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":"2026-05-18T04:34:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VO5xgkDeWLDH6qON81aOymafmYEyTsl0u2S4SmEsZjQTfXS9yZ4evM9IfpR8XyX/k51k1rLAkgCHZ5E5B54ACQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T04:16:46.673686Z"},"content_sha256":"87314021815069c44300669638b263079b9829e20c63af018dcbe38f6c93e70f","schema_version":"1.0","event_id":"sha256:87314021815069c44300669638b263079b9829e20c63af018dcbe38f6c93e70f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/DBUVE4BAXRNAAICRE3QO5BRBY2/bundle.json","state_url":"https://pith.science/pith/DBUVE4BAXRNAAICRE3QO5BRBY2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/DBUVE4BAXRNAAICRE3QO5BRBY2/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":"2026-06-24T04:16:46Z","links":{"resolver":"https://pith.science/pith/DBUVE4BAXRNAAICRE3QO5BRBY2","bundle":"https://pith.science/pith/DBUVE4BAXRNAAICRE3QO5BRBY2/bundle.json","state":"https://pith.science/pith/DBUVE4BAXRNAAICRE3QO5BRBY2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/DBUVE4BAXRNAAICRE3QO5BRBY2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:DBUVE4BAXRNAAICRE3QO5BRBY2","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":"36f8a6af3a28194aaa1f9e33f45877017b69f136b0bb553425888f49fda586e6","cross_cats_sorted":["cs.FL","nlin.CG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2010-12-03T09:41:17Z","title_canon_sha256":"398f7a472f5e2af1f632a9a31ad74b886127d23f9ed2f22958da95953595a483"},"schema_version":"1.0","source":{"id":"1012.1332","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1012.1332","created_at":"2026-05-18T04:34:01Z"},{"alias_kind":"arxiv_version","alias_value":"1012.1332v1","created_at":"2026-05-18T04:34:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1012.1332","created_at":"2026-05-18T04:34:01Z"},{"alias_kind":"pith_short_12","alias_value":"DBUVE4BAXRNA","created_at":"2026-05-18T12:26:06Z"},{"alias_kind":"pith_short_16","alias_value":"DBUVE4BAXRNAAICR","created_at":"2026-05-18T12:26:06Z"},{"alias_kind":"pith_short_8","alias_value":"DBUVE4BA","created_at":"2026-05-18T12:26:06Z"}],"graph_snapshots":[{"event_id":"sha256:87314021815069c44300669638b263079b9829e20c63af018dcbe38f6c93e70f","target":"graph","created_at":"2026-05-18T04:34:01Z","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"},"paper":{"abstract_excerpt":"Together with the concept of reversibility, another relevant physical notion is time-symmetry, which expresses that there is no way of distinguishing between backward and forward time directions. This notion, found in physical theories, has been neglected in the area of discrete dynamical systems. Here we formalize it in the context of cellular automata and establish some basic facts and relations. We also state some open problems that may encourage further research on the topic.","authors_text":"Anahi Gajardo, Andr\\'es Moreira","cross_cats":["cs.FL","nlin.CG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2010-12-03T09:41:17Z","title":"Time-Symmetric Cellular Automata"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1012.1332","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":"sha256:001c3a5327173ca672013449561ea8660f37cb77130686e60a40d36427c22272","target":"record","created_at":"2026-05-18T04:34:01Z","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":"36f8a6af3a28194aaa1f9e33f45877017b69f136b0bb553425888f49fda586e6","cross_cats_sorted":["cs.FL","nlin.CG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2010-12-03T09:41:17Z","title_canon_sha256":"398f7a472f5e2af1f632a9a31ad74b886127d23f9ed2f22958da95953595a483"},"schema_version":"1.0","source":{"id":"1012.1332","kind":"arxiv","version":1}},"canonical_sha256":"1869527020bc5a00205126e0ee8621c6a4f2463ad5f36061e82303ccc8809cac","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1869527020bc5a00205126e0ee8621c6a4f2463ad5f36061e82303ccc8809cac","first_computed_at":"2026-05-18T04:34:01.176671Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:34:01.176671Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"8HgK0eamNsrd47X/wNI+1KIfdtPUrimphJgiqDI8m8rUL4SDBjW51M5x6dcIoauEaaBOwtUD3ZtiL6/dkwX3CA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:34:01.177050Z","signed_message":"canonical_sha256_bytes"},"source_id":"1012.1332","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:001c3a5327173ca672013449561ea8660f37cb77130686e60a40d36427c22272","sha256:87314021815069c44300669638b263079b9829e20c63af018dcbe38f6c93e70f"],"state_sha256":"185dd8eaef080acbb98ab3deffb7f10045be3f1d6bc739c404b19ec007092317"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ft3adnMPy5+QdyQc0PW2PzxsbSGm4h8o4EH9s6fnmbawRiL8UDX6UGPthW6/7PtNragMNCJlYm7R1aJp1iTYDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-24T04:16:46.675571Z","bundle_sha256":"8ff0c2070d69d7f055473db34d20c1a9866a65863444b80c708fc606344d61d6"}}