{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2023:AINEAZMUHBWSU3EH3BOZEY4T2A","short_pith_number":"pith:AINEAZMU","canonical_record":{"source":{"id":"2309.15468","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2023-09-27T08:04:40Z","cross_cats_sorted":["nlin.CG"],"title_canon_sha256":"c97e793df06aad0f0330b1799b08d5d5e5559eb2f6cf5d2446146933d7e2c957","abstract_canon_sha256":"7d6e32b25df8230571fb3c201536dc42397eb089abd054f514dd28908edd2f7b"},"schema_version":"1.0"},"canonical_sha256":"021a406594386d2a6c87d85d926393d03daf4bf94cedea73c17ae9ef88c40ba8","source":{"kind":"arxiv","id":"2309.15468","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2309.15468","created_at":"2026-07-05T06:54:46Z"},{"alias_kind":"arxiv_version","alias_value":"2309.15468v1","created_at":"2026-07-05T06:54:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2309.15468","created_at":"2026-07-05T06:54:46Z"},{"alias_kind":"pith_short_12","alias_value":"AINEAZMUHBWS","created_at":"2026-07-05T06:54:46Z"},{"alias_kind":"pith_short_16","alias_value":"AINEAZMUHBWSU3EH","created_at":"2026-07-05T06:54:46Z"},{"alias_kind":"pith_short_8","alias_value":"AINEAZMU","created_at":"2026-07-05T06:54:46Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2023:AINEAZMUHBWSU3EH3BOZEY4T2A","target":"record","payload":{"canonical_record":{"source":{"id":"2309.15468","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2023-09-27T08:04:40Z","cross_cats_sorted":["nlin.CG"],"title_canon_sha256":"c97e793df06aad0f0330b1799b08d5d5e5559eb2f6cf5d2446146933d7e2c957","abstract_canon_sha256":"7d6e32b25df8230571fb3c201536dc42397eb089abd054f514dd28908edd2f7b"},"schema_version":"1.0"},"canonical_sha256":"021a406594386d2a6c87d85d926393d03daf4bf94cedea73c17ae9ef88c40ba8","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T06:54:46.312518Z","signature_b64":"rXYbszgM22S7j4T3g3HbRWz2sGhDLQ4/Zixs3FbmbZXpQ2EskMZ1ykUyRMtLhX8aSpeSaNpEreK0W8pP67guBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"021a406594386d2a6c87d85d926393d03daf4bf94cedea73c17ae9ef88c40ba8","last_reissued_at":"2026-07-05T06:54:46.311996Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T06:54:46.311996Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2309.15468","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":"2026-07-05T06:54:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sNuXhMZqn0nMaNQB6T6zbI64rJKaBmqADIyWOaAhvfYRt+44hAFJn07RQzGL9s6VQpAmjt/ou9igzwP8YSlBBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-17T19:10:38.207838Z"},"content_sha256":"2488010b9b2a90d91210920242f8ce715dc09a4db52ede4ab0e84a43293f83eb","schema_version":"1.0","event_id":"sha256:2488010b9b2a90d91210920242f8ce715dc09a4db52ede4ab0e84a43293f83eb"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2023:AINEAZMUHBWSU3EH3BOZEY4T2A","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Patterns Induce Injectivity: A New Thinking in Constructing Injective Local Rules of 1D Cellular Automata over $\\mathbb{F}_2$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["nlin.CG"],"primary_cat":"cs.CC","authors_text":"Chao Wang, Chen Wang, Defu Lin, Junchi Ma, Weilin Chen","submitted_at":"2023-09-27T08:04:40Z","abstract_excerpt":"We discovered that certain patterns called injective patterns remain stable during the revolution process, allowing us to create many reversible CA simply by using them to design the revolution rules. By examining injective patterns, we investigated their structural stability during revolutions. This led us to discover extended patterns and pattern mixtures that can create more reversible cellular automata. Furthermore, our research proposed a new way to study the reversibility of CA by observing the structure of local rule $f$. In this paper, we will explicate our study and propose an efficie"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2309.15468","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/2309.15468/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":"2026-07-05T06:54:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OH8gP9U6yxLaAW4HuMjx1EReGHSMu+m0fMZDOJh2sBBvOQj8z1noo2eeHRL33+GQviFzkf+9k3wzqrgQtZOECw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-17T19:10:38.208359Z"},"content_sha256":"95dad996d43fd004b3430471e3e5ce4335d603fc86abb460a7de4ba1889c1d17","schema_version":"1.0","event_id":"sha256:95dad996d43fd004b3430471e3e5ce4335d603fc86abb460a7de4ba1889c1d17"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/AINEAZMUHBWSU3EH3BOZEY4T2A/bundle.json","state_url":"https://pith.science/pith/AINEAZMUHBWSU3EH3BOZEY4T2A/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/AINEAZMUHBWSU3EH3BOZEY4T2A/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":"2026-08-17T19:10:38Z","links":{"resolver":"https://pith.science/pith/AINEAZMUHBWSU3EH3BOZEY4T2A","bundle":"https://pith.science/pith/AINEAZMUHBWSU3EH3BOZEY4T2A/bundle.json","state":"https://pith.science/pith/AINEAZMUHBWSU3EH3BOZEY4T2A/state.json","well_known_bundle":"https://pith.science/.well-known/pith/AINEAZMUHBWSU3EH3BOZEY4T2A/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:AINEAZMUHBWSU3EH3BOZEY4T2A","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":"7d6e32b25df8230571fb3c201536dc42397eb089abd054f514dd28908edd2f7b","cross_cats_sorted":["nlin.CG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2023-09-27T08:04:40Z","title_canon_sha256":"c97e793df06aad0f0330b1799b08d5d5e5559eb2f6cf5d2446146933d7e2c957"},"schema_version":"1.0","source":{"id":"2309.15468","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2309.15468","created_at":"2026-07-05T06:54:46Z"},{"alias_kind":"arxiv_version","alias_value":"2309.15468v1","created_at":"2026-07-05T06:54:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2309.15468","created_at":"2026-07-05T06:54:46Z"},{"alias_kind":"pith_short_12","alias_value":"AINEAZMUHBWS","created_at":"2026-07-05T06:54:46Z"},{"alias_kind":"pith_short_16","alias_value":"AINEAZMUHBWSU3EH","created_at":"2026-07-05T06:54:46Z"},{"alias_kind":"pith_short_8","alias_value":"AINEAZMU","created_at":"2026-07-05T06:54:46Z"}],"graph_snapshots":[{"event_id":"sha256:95dad996d43fd004b3430471e3e5ce4335d603fc86abb460a7de4ba1889c1d17","target":"graph","created_at":"2026-07-05T06:54:46Z","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/2309.15468/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We discovered that certain patterns called injective patterns remain stable during the revolution process, allowing us to create many reversible CA simply by using them to design the revolution rules. By examining injective patterns, we investigated their structural stability during revolutions. This led us to discover extended patterns and pattern mixtures that can create more reversible cellular automata. Furthermore, our research proposed a new way to study the reversibility of CA by observing the structure of local rule $f$. In this paper, we will explicate our study and propose an efficie","authors_text":"Chao Wang, Chen Wang, Defu Lin, Junchi Ma, Weilin Chen","cross_cats":["nlin.CG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2023-09-27T08:04:40Z","title":"Patterns Induce Injectivity: A New Thinking in Constructing Injective Local Rules of 1D Cellular Automata over $\\mathbb{F}_2$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2309.15468","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":"sha256:2488010b9b2a90d91210920242f8ce715dc09a4db52ede4ab0e84a43293f83eb","target":"record","created_at":"2026-07-05T06:54:46Z","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":"7d6e32b25df8230571fb3c201536dc42397eb089abd054f514dd28908edd2f7b","cross_cats_sorted":["nlin.CG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2023-09-27T08:04:40Z","title_canon_sha256":"c97e793df06aad0f0330b1799b08d5d5e5559eb2f6cf5d2446146933d7e2c957"},"schema_version":"1.0","source":{"id":"2309.15468","kind":"arxiv","version":1}},"canonical_sha256":"021a406594386d2a6c87d85d926393d03daf4bf94cedea73c17ae9ef88c40ba8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"021a406594386d2a6c87d85d926393d03daf4bf94cedea73c17ae9ef88c40ba8","first_computed_at":"2026-07-05T06:54:46.311996Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T06:54:46.311996Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"rXYbszgM22S7j4T3g3HbRWz2sGhDLQ4/Zixs3FbmbZXpQ2EskMZ1ykUyRMtLhX8aSpeSaNpEreK0W8pP67guBQ==","signature_status":"signed_v1","signed_at":"2026-07-05T06:54:46.312518Z","signed_message":"canonical_sha256_bytes"},"source_id":"2309.15468","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2488010b9b2a90d91210920242f8ce715dc09a4db52ede4ab0e84a43293f83eb","sha256:95dad996d43fd004b3430471e3e5ce4335d603fc86abb460a7de4ba1889c1d17"],"state_sha256":"ef54120146809e5e6da3b75f08ee603d4a340cf37834dc95c429fff4548256da"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3wVgssXb46gsuD3jY2HRTcMyazi/jDZweu0FsCX+EnjMFRQDFzllYWY934njCUn+XdJVwwJIePxyqPSurlOrAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-17T19:10:38.214156Z","bundle_sha256":"9f7c356684756321c0fd4026bb4a7aa2f8936af39ee59db8b03b6057aba64788"}}