{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:AWFIVQ4SWK53MNRZTZQEDGUX4Q","short_pith_number":"pith:AWFIVQ4S","canonical_record":{"source":{"id":"2606.12331","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2026-06-10T17:04:32Z","cross_cats_sorted":["math.GT"],"title_canon_sha256":"e679244d7ee9d2747cfae33bc16a825c3e13d2a9e17b40bbe3047231f5ab3353","abstract_canon_sha256":"705cd6d946e4dcf6d6058e31a0de6fb5b3d1b62a61ce07db7374187718590d5d"},"schema_version":"1.0"},"canonical_sha256":"058a8ac392b2bbb636399e60419a97e41e706091a4dad4294a82de16c1499da7","source":{"kind":"arxiv","id":"2606.12331","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.12331","created_at":"2026-06-11T01:11:02Z"},{"alias_kind":"arxiv_version","alias_value":"2606.12331v1","created_at":"2026-06-11T01:11:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.12331","created_at":"2026-06-11T01:11:02Z"},{"alias_kind":"pith_short_12","alias_value":"AWFIVQ4SWK53","created_at":"2026-06-11T01:11:02Z"},{"alias_kind":"pith_short_16","alias_value":"AWFIVQ4SWK53MNRZ","created_at":"2026-06-11T01:11:02Z"},{"alias_kind":"pith_short_8","alias_value":"AWFIVQ4S","created_at":"2026-06-11T01:11:02Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:AWFIVQ4SWK53MNRZTZQEDGUX4Q","target":"record","payload":{"canonical_record":{"source":{"id":"2606.12331","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2026-06-10T17:04:32Z","cross_cats_sorted":["math.GT"],"title_canon_sha256":"e679244d7ee9d2747cfae33bc16a825c3e13d2a9e17b40bbe3047231f5ab3353","abstract_canon_sha256":"705cd6d946e4dcf6d6058e31a0de6fb5b3d1b62a61ce07db7374187718590d5d"},"schema_version":"1.0"},"canonical_sha256":"058a8ac392b2bbb636399e60419a97e41e706091a4dad4294a82de16c1499da7","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-11T01:11:02.197189Z","signature_b64":"L97OSGQCcOBlsoxWjbpdeTCfXU+YC4xRBeG88nc9lCur/OtUKWW9tbPaVellba4NK3rCmGiCQDN3/YLdehUyDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"058a8ac392b2bbb636399e60419a97e41e706091a4dad4294a82de16c1499da7","last_reissued_at":"2026-06-11T01:11:02.196257Z","signature_status":"signed_v1","first_computed_at":"2026-06-11T01:11:02.196257Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2606.12331","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":"2026-06-11T01:11:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Fxwp+AsSWyIyJcXiawjwu55U8Qjv6g3hOoYmdvaAmszPBu99zlGwuoxBr6l5s/bIdDqGw32eRPx0cyLIU0a3Cw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T20:24:51.870833Z"},"content_sha256":"25210e08cf2008c603813152f89e46c60df3879ad8de5e9fec6b222f7243d039","schema_version":"1.0","event_id":"sha256:25210e08cf2008c603813152f89e46c60df3879ad8de5e9fec6b222f7243d039"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:AWFIVQ4SWK53MNRZTZQEDGUX4Q","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Resolving the Schwartz Quadratic Meander Number Conjecture","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.GT"],"primary_cat":"math.CO","authors_text":"Charles Daly, Diaaeldin Taha","submitted_at":"2026-06-10T17:04:32Z","abstract_excerpt":"A cyclic meander is an embedded oriented loop in the plane intersecting a fixed infinite line, or circle, transversely in a linearly ordered set of $2n$ points. By keeping track of the order in which the loop visits these points, the cyclic meander induces a cyclic permutation on these marked points. Correspondingly, given a permutation on $n$ letters, one can ask whether or not a cyclic meander induces the permutation in this manner, and if not, what is the most efficient way of doing so if we allow more points of intersection? This process gives a way of associating to a permutation on $n$ l"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.12331","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/2606.12331/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":"2026-06-11T01:11:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9p414hmaAThIpfYTOtTGXLeNFlQagmCDw73DElsr9o+JJ4I07uE1LPH4zB0Sl7Nf0Z7dNtg59X8vUCFkTzyJCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T20:24:51.871214Z"},"content_sha256":"e3bb3d2d57e17b5f05d226ca50aaf43cbd9f36d2be32fb448c40d4742ebc40bf","schema_version":"1.0","event_id":"sha256:e3bb3d2d57e17b5f05d226ca50aaf43cbd9f36d2be32fb448c40d4742ebc40bf"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/AWFIVQ4SWK53MNRZTZQEDGUX4Q/bundle.json","state_url":"https://pith.science/pith/AWFIVQ4SWK53MNRZTZQEDGUX4Q/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/AWFIVQ4SWK53MNRZTZQEDGUX4Q/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":"2026-06-22T20:24:51Z","links":{"resolver":"https://pith.science/pith/AWFIVQ4SWK53MNRZTZQEDGUX4Q","bundle":"https://pith.science/pith/AWFIVQ4SWK53MNRZTZQEDGUX4Q/bundle.json","state":"https://pith.science/pith/AWFIVQ4SWK53MNRZTZQEDGUX4Q/state.json","well_known_bundle":"https://pith.science/.well-known/pith/AWFIVQ4SWK53MNRZTZQEDGUX4Q/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:AWFIVQ4SWK53MNRZTZQEDGUX4Q","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":"705cd6d946e4dcf6d6058e31a0de6fb5b3d1b62a61ce07db7374187718590d5d","cross_cats_sorted":["math.GT"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2026-06-10T17:04:32Z","title_canon_sha256":"e679244d7ee9d2747cfae33bc16a825c3e13d2a9e17b40bbe3047231f5ab3353"},"schema_version":"1.0","source":{"id":"2606.12331","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.12331","created_at":"2026-06-11T01:11:02Z"},{"alias_kind":"arxiv_version","alias_value":"2606.12331v1","created_at":"2026-06-11T01:11:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.12331","created_at":"2026-06-11T01:11:02Z"},{"alias_kind":"pith_short_12","alias_value":"AWFIVQ4SWK53","created_at":"2026-06-11T01:11:02Z"},{"alias_kind":"pith_short_16","alias_value":"AWFIVQ4SWK53MNRZ","created_at":"2026-06-11T01:11:02Z"},{"alias_kind":"pith_short_8","alias_value":"AWFIVQ4S","created_at":"2026-06-11T01:11:02Z"}],"graph_snapshots":[{"event_id":"sha256:e3bb3d2d57e17b5f05d226ca50aaf43cbd9f36d2be32fb448c40d4742ebc40bf","target":"graph","created_at":"2026-06-11T01:11:02Z","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/2606.12331/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"A cyclic meander is an embedded oriented loop in the plane intersecting a fixed infinite line, or circle, transversely in a linearly ordered set of $2n$ points. By keeping track of the order in which the loop visits these points, the cyclic meander induces a cyclic permutation on these marked points. Correspondingly, given a permutation on $n$ letters, one can ask whether or not a cyclic meander induces the permutation in this manner, and if not, what is the most efficient way of doing so if we allow more points of intersection? This process gives a way of associating to a permutation on $n$ l","authors_text":"Charles Daly, Diaaeldin Taha","cross_cats":["math.GT"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2026-06-10T17:04:32Z","title":"Resolving the Schwartz Quadratic Meander Number Conjecture"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.12331","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":"sha256:25210e08cf2008c603813152f89e46c60df3879ad8de5e9fec6b222f7243d039","target":"record","created_at":"2026-06-11T01:11:02Z","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":"705cd6d946e4dcf6d6058e31a0de6fb5b3d1b62a61ce07db7374187718590d5d","cross_cats_sorted":["math.GT"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2026-06-10T17:04:32Z","title_canon_sha256":"e679244d7ee9d2747cfae33bc16a825c3e13d2a9e17b40bbe3047231f5ab3353"},"schema_version":"1.0","source":{"id":"2606.12331","kind":"arxiv","version":1}},"canonical_sha256":"058a8ac392b2bbb636399e60419a97e41e706091a4dad4294a82de16c1499da7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"058a8ac392b2bbb636399e60419a97e41e706091a4dad4294a82de16c1499da7","first_computed_at":"2026-06-11T01:11:02.196257Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-11T01:11:02.196257Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"L97OSGQCcOBlsoxWjbpdeTCfXU+YC4xRBeG88nc9lCur/OtUKWW9tbPaVellba4NK3rCmGiCQDN3/YLdehUyDA==","signature_status":"signed_v1","signed_at":"2026-06-11T01:11:02.197189Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.12331","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:25210e08cf2008c603813152f89e46c60df3879ad8de5e9fec6b222f7243d039","sha256:e3bb3d2d57e17b5f05d226ca50aaf43cbd9f36d2be32fb448c40d4742ebc40bf"],"state_sha256":"6d69dbac4c4b3b54a657ef3a5e196d016ed3151c37f6c69ab98f55bb61da6dee"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"O4YKq8P5HJ+mHdms6TcgrIfXJGm0qvZlK5eqPW2x21wDqasPG0w6zOxl5L9Kd5BQ85pcKERoyrmbrTqu4TVVDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-22T20:24:51.873250Z","bundle_sha256":"304dbd27c76308f90ab9845653af59f8764a403ce58d1321ef2569accc82f306"}}