{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:CDHGUZS2G3QUECLTCUWFPMOZK4","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":"6286d2566b78cd463c53d04ce9ad16df31552f875ab38557b82f8f7d9a1d0515","cross_cats_sorted":["cs.CC","math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2026-07-10T22:58:55Z","title_canon_sha256":"6563122dc00735d30d9a31524b06f8b3eb3b96ba39c9c2ceeeb8bbc53d097da3"},"schema_version":"1.0","source":{"id":"2607.10022","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.10022","created_at":"2026-07-14T00:18:47Z"},{"alias_kind":"arxiv_version","alias_value":"2607.10022v1","created_at":"2026-07-14T00:18:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.10022","created_at":"2026-07-14T00:18:47Z"},{"alias_kind":"pith_short_12","alias_value":"CDHGUZS2G3QU","created_at":"2026-07-14T00:18:47Z"},{"alias_kind":"pith_short_16","alias_value":"CDHGUZS2G3QUECLT","created_at":"2026-07-14T00:18:47Z"},{"alias_kind":"pith_short_8","alias_value":"CDHGUZS2","created_at":"2026-07-14T00:18:47Z"}],"graph_snapshots":[{"event_id":"sha256:666e26b41b851127b542d56dbef05552bdeffc45e134974c9b1c86b08f142633","target":"graph","created_at":"2026-07-14T00:18:47Z","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/2607.10022/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We prove that, given any contact $3$-manifold and any computable function $f: \\mathbb{N} \\dashrightarrow \\mathbb{N}$, there exists a defining contact form and a Poincar\\'e section of its Reeb flow whose partially defined return map computes $f$.","authors_text":"\\'Angel Gonz\\'alez-Prieto, Eva Miranda, Kai Cieliebak","cross_cats":["cs.CC","math.DS"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2026-07-10T22:58:55Z","title":"Computable functions as Reeb flows"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.10022","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:cdd072aa68c0979d5f166334a0b1efea03be16b7cc44741dc8cde3e9ffe53abb","target":"record","created_at":"2026-07-14T00:18:47Z","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":"6286d2566b78cd463c53d04ce9ad16df31552f875ab38557b82f8f7d9a1d0515","cross_cats_sorted":["cs.CC","math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2026-07-10T22:58:55Z","title_canon_sha256":"6563122dc00735d30d9a31524b06f8b3eb3b96ba39c9c2ceeeb8bbc53d097da3"},"schema_version":"1.0","source":{"id":"2607.10022","kind":"arxiv","version":1}},"canonical_sha256":"10ce6a665a36e1420973152c57b1d957370570fd5deb9f42e8a3901e8eb81d5b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"10ce6a665a36e1420973152c57b1d957370570fd5deb9f42e8a3901e8eb81d5b","first_computed_at":"2026-07-14T00:18:47.993785Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-14T00:18:47.993785Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"CUnA4FhdVjVQYF/IIWwmA2CaKSKYzbPCYzsfQDgUJNrUhOl3Jlfq9Evxae0gYSNOyAVoPNCuDT5rsS+tw6XJCQ==","signature_status":"signed_v1","signed_at":"2026-07-14T00:18:47.994537Z","signed_message":"canonical_sha256_bytes"},"source_id":"2607.10022","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cdd072aa68c0979d5f166334a0b1efea03be16b7cc44741dc8cde3e9ffe53abb","sha256:666e26b41b851127b542d56dbef05552bdeffc45e134974c9b1c86b08f142633"],"state_sha256":"ce652f60d9d4a28e96d4fcaa50d7458f4a0371d62164b8476a8b15ce65d6862c"}