{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:4MKJCEKEQJ5DMGS3QBFNXRBCGL","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":"3414d5ee0df7b984a81e716bc6ce6de41a2b5582db39720c1b6e6bb8375d7dfd","cross_cats_sorted":["cs.PL"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LO","submitted_at":"2026-06-15T19:21:16Z","title_canon_sha256":"1bfa83ef07a83bb49345fb54c9fc59d403b478b7b0fda4d6e0e91c295a259843"},"schema_version":"1.0","source":{"id":"2606.17228","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.17228","created_at":"2026-06-19T16:10:06Z"},{"alias_kind":"arxiv_version","alias_value":"2606.17228v1","created_at":"2026-06-19T16:10:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.17228","created_at":"2026-06-19T16:10:06Z"},{"alias_kind":"pith_short_12","alias_value":"4MKJCEKEQJ5D","created_at":"2026-06-19T16:10:06Z"},{"alias_kind":"pith_short_16","alias_value":"4MKJCEKEQJ5DMGS3","created_at":"2026-06-19T16:10:06Z"},{"alias_kind":"pith_short_8","alias_value":"4MKJCEKE","created_at":"2026-06-19T16:10:06Z"}],"graph_snapshots":[{"event_id":"sha256:aa229122e036e1f07f82fa528be9c08628087ddfab277577c741c2f5f5ef0cda","target":"graph","created_at":"2026-06-19T16:10:06Z","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/2606.17228/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"This paper develops a compact collecting semantics for the residual behaviour left by nonterminating computation. For sequential time this is the tail-cluster set of the stream in the Stone-Cech compactification of the observation space. It gives a common semantics to ordinary recurrence, mixed recurrent behaviour, and escape through noncompact parts of the observation space.\n  The basic theory establishes tail invariance, functoriality under continuous observations, and a temporal reading for clopen observations: containment in the corresponding clopen region of beta-X is eventual truth, whil","authors_text":"Mike Stannett","cross_cats":["cs.PL"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LO","submitted_at":"2026-06-15T19:21:16Z","title":"A Stone-Cech Collecting Semantics for Residual Process Behaviour"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.17228","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":"sha256:12f4a0e7b4be9424761b52b87a75c9265ae47778596161d65a82bf5da315238a","target":"record","created_at":"2026-06-19T16:10:06Z","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":"3414d5ee0df7b984a81e716bc6ce6de41a2b5582db39720c1b6e6bb8375d7dfd","cross_cats_sorted":["cs.PL"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LO","submitted_at":"2026-06-15T19:21:16Z","title_canon_sha256":"1bfa83ef07a83bb49345fb54c9fc59d403b478b7b0fda4d6e0e91c295a259843"},"schema_version":"1.0","source":{"id":"2606.17228","kind":"arxiv","version":1}},"canonical_sha256":"e314911144827a361a5b804adbc42232c3c38f7bd1f1a8f521395e08f21e7c95","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e314911144827a361a5b804adbc42232c3c38f7bd1f1a8f521395e08f21e7c95","first_computed_at":"2026-06-19T16:10:06.428282Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-19T16:10:06.428282Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"5uFHk4lzQ6FgX1Af16qKfjNRTSWXmmepJXPleNGB++v3oYoazUxitNHO2GfgKJF2q6FAUNbAgdrUAZk31q8tCQ==","signature_status":"signed_v1","signed_at":"2026-06-19T16:10:06.428701Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.17228","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:12f4a0e7b4be9424761b52b87a75c9265ae47778596161d65a82bf5da315238a","sha256:aa229122e036e1f07f82fa528be9c08628087ddfab277577c741c2f5f5ef0cda"],"state_sha256":"0e38c7905f9fa5daf0ccefe4df94d79e5246bc1bcfd5311863918410a47382d6"}