{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:F4IMBU2N5CB3ORLZS2Z7LEUFT3","short_pith_number":"pith:F4IMBU2N","canonical_record":{"source":{"id":"2606.30270","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2026-06-29T13:17:52Z","cross_cats_sorted":["cs.DM","math.DS"],"title_canon_sha256":"1ea80511b2ebb9dd7a3ae4146cecce0fcab11d37cc37b2d9bd49163a6c015e9f","abstract_canon_sha256":"1dcdec0d1f7d28c267b11a021a0e3cdf9d18c864ebade33d591c17cf29a56bab"},"schema_version":"1.0"},"canonical_sha256":"2f10c0d34de883b7457996b3f592859ef679f9fc0cd28e87b9de09fa9176ac66","source":{"kind":"arxiv","id":"2606.30270","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.30270","created_at":"2026-06-30T02:17:56Z"},{"alias_kind":"arxiv_version","alias_value":"2606.30270v1","created_at":"2026-06-30T02:17:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.30270","created_at":"2026-06-30T02:17:56Z"},{"alias_kind":"pith_short_12","alias_value":"F4IMBU2N5CB3","created_at":"2026-06-30T02:17:56Z"},{"alias_kind":"pith_short_16","alias_value":"F4IMBU2N5CB3ORLZ","created_at":"2026-06-30T02:17:56Z"},{"alias_kind":"pith_short_8","alias_value":"F4IMBU2N","created_at":"2026-06-30T02:17:56Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:F4IMBU2N5CB3ORLZS2Z7LEUFT3","target":"record","payload":{"canonical_record":{"source":{"id":"2606.30270","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2026-06-29T13:17:52Z","cross_cats_sorted":["cs.DM","math.DS"],"title_canon_sha256":"1ea80511b2ebb9dd7a3ae4146cecce0fcab11d37cc37b2d9bd49163a6c015e9f","abstract_canon_sha256":"1dcdec0d1f7d28c267b11a021a0e3cdf9d18c864ebade33d591c17cf29a56bab"},"schema_version":"1.0"},"canonical_sha256":"2f10c0d34de883b7457996b3f592859ef679f9fc0cd28e87b9de09fa9176ac66","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-30T02:17:56.876302Z","signature_b64":"szgLCheqvIVWPcW9a49T+p9NkyPiFJq3Tm+JNxJVpoHo7vCJ217ljweQ5p41tm49oTUkDIrZBkHEqt5xV6gvAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2f10c0d34de883b7457996b3f592859ef679f9fc0cd28e87b9de09fa9176ac66","last_reissued_at":"2026-06-30T02:17:56.875649Z","signature_status":"signed_v1","first_computed_at":"2026-06-30T02:17:56.875649Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2606.30270","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":"2026-06-30T02:17:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ljiF+LUYAbVba4spAddTdTaM2RScHGVk/Tdzr+I7JF5Nb6E6JL32C6IJzDbOE9MLuuW4Op04TvmDdcim8uSPDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-30T14:58:20.118657Z"},"content_sha256":"d5f33101fac4a8443913b8375e196a56dba2b1e87efc71a648fa78a20d417fca","schema_version":"1.0","event_id":"sha256:d5f33101fac4a8443913b8375e196a56dba2b1e87efc71a648fa78a20d417fca"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:F4IMBU2N5CB3ORLZS2Z7LEUFT3","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Cyclic Attractor Detection in Boolean Network Dynamics under Local Logical Constraints","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM","math.DS"],"primary_cat":"cs.CC","authors_text":"Alexander Drobyshev, Grigoriy Bokov","submitted_at":"2026-06-29T13:17:52Z","abstract_excerpt":"Boolean networks are finite discrete nonlinear systems whose long-term behaviour is organised by fixed-point and cyclic attractors. Detecting such recurrent states is important in applications ranging from gene regulation and neural computation to complex-network models, but the computational boundary between tractable and intractable attractor analysis is still not fully understood. We study that boundary from the perspective of local logical rules. We consider Boolean networks under parallel update whose coordinate functions are given by circuits over a fixed finite basis of a closed Boolean"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.30270","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/2606.30270/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":"2026-06-30T02:17:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"syRaDCzqCILaNQXusSBOI8DuhepmlDbr+s+p0U+s8sNp2fYBqs7J0CZRGMn50VK2xHPk+/9C5yTaPxcxVPceCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-30T14:58:20.119030Z"},"content_sha256":"f82c175015f7e5f93fcdaa19961b7f8cf15657cd4ba57164d72f79c89304a14a","schema_version":"1.0","event_id":"sha256:f82c175015f7e5f93fcdaa19961b7f8cf15657cd4ba57164d72f79c89304a14a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/F4IMBU2N5CB3ORLZS2Z7LEUFT3/bundle.json","state_url":"https://pith.science/pith/F4IMBU2N5CB3ORLZS2Z7LEUFT3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/F4IMBU2N5CB3ORLZS2Z7LEUFT3/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":"2026-06-30T14:58:20Z","links":{"resolver":"https://pith.science/pith/F4IMBU2N5CB3ORLZS2Z7LEUFT3","bundle":"https://pith.science/pith/F4IMBU2N5CB3ORLZS2Z7LEUFT3/bundle.json","state":"https://pith.science/pith/F4IMBU2N5CB3ORLZS2Z7LEUFT3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/F4IMBU2N5CB3ORLZS2Z7LEUFT3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:F4IMBU2N5CB3ORLZS2Z7LEUFT3","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":"1dcdec0d1f7d28c267b11a021a0e3cdf9d18c864ebade33d591c17cf29a56bab","cross_cats_sorted":["cs.DM","math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2026-06-29T13:17:52Z","title_canon_sha256":"1ea80511b2ebb9dd7a3ae4146cecce0fcab11d37cc37b2d9bd49163a6c015e9f"},"schema_version":"1.0","source":{"id":"2606.30270","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.30270","created_at":"2026-06-30T02:17:56Z"},{"alias_kind":"arxiv_version","alias_value":"2606.30270v1","created_at":"2026-06-30T02:17:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.30270","created_at":"2026-06-30T02:17:56Z"},{"alias_kind":"pith_short_12","alias_value":"F4IMBU2N5CB3","created_at":"2026-06-30T02:17:56Z"},{"alias_kind":"pith_short_16","alias_value":"F4IMBU2N5CB3ORLZ","created_at":"2026-06-30T02:17:56Z"},{"alias_kind":"pith_short_8","alias_value":"F4IMBU2N","created_at":"2026-06-30T02:17:56Z"}],"graph_snapshots":[{"event_id":"sha256:f82c175015f7e5f93fcdaa19961b7f8cf15657cd4ba57164d72f79c89304a14a","target":"graph","created_at":"2026-06-30T02:17:56Z","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/2606.30270/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Boolean networks are finite discrete nonlinear systems whose long-term behaviour is organised by fixed-point and cyclic attractors. Detecting such recurrent states is important in applications ranging from gene regulation and neural computation to complex-network models, but the computational boundary between tractable and intractable attractor analysis is still not fully understood. We study that boundary from the perspective of local logical rules. We consider Boolean networks under parallel update whose coordinate functions are given by circuits over a fixed finite basis of a closed Boolean","authors_text":"Alexander Drobyshev, Grigoriy Bokov","cross_cats":["cs.DM","math.DS"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2026-06-29T13:17:52Z","title":"Cyclic Attractor Detection in Boolean Network Dynamics under Local Logical Constraints"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.30270","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:d5f33101fac4a8443913b8375e196a56dba2b1e87efc71a648fa78a20d417fca","target":"record","created_at":"2026-06-30T02:17:56Z","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":"1dcdec0d1f7d28c267b11a021a0e3cdf9d18c864ebade33d591c17cf29a56bab","cross_cats_sorted":["cs.DM","math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2026-06-29T13:17:52Z","title_canon_sha256":"1ea80511b2ebb9dd7a3ae4146cecce0fcab11d37cc37b2d9bd49163a6c015e9f"},"schema_version":"1.0","source":{"id":"2606.30270","kind":"arxiv","version":1}},"canonical_sha256":"2f10c0d34de883b7457996b3f592859ef679f9fc0cd28e87b9de09fa9176ac66","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2f10c0d34de883b7457996b3f592859ef679f9fc0cd28e87b9de09fa9176ac66","first_computed_at":"2026-06-30T02:17:56.875649Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-30T02:17:56.875649Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"szgLCheqvIVWPcW9a49T+p9NkyPiFJq3Tm+JNxJVpoHo7vCJ217ljweQ5p41tm49oTUkDIrZBkHEqt5xV6gvAQ==","signature_status":"signed_v1","signed_at":"2026-06-30T02:17:56.876302Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.30270","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d5f33101fac4a8443913b8375e196a56dba2b1e87efc71a648fa78a20d417fca","sha256:f82c175015f7e5f93fcdaa19961b7f8cf15657cd4ba57164d72f79c89304a14a"],"state_sha256":"d3fc36529a8a1862bc30da54932fef3b4830002797c93cbb96cbad7cded453d2"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"k/kC9UImu3/gG32i6kGmEctwGPcmr8VnOA5BGLsxSLXAxBd8rW0Hq3wopsKNXKzHLNuNNDqX+tr+1K9vKRDhBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-30T14:58:20.121028Z","bundle_sha256":"ec1d3c8e3e00135d3b5aa7777c3f818115f82db857d4714ec6bac67769b343cf"}}