{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:HWISG632UTNZXNMVPTXVIW2O2T","short_pith_number":"pith:HWISG632","schema_version":"1.0","canonical_sha256":"3d91237b7aa4db9bb5957cef545b4ed4d49d8499dbb5fbbfbe44eed085398260","source":{"kind":"arxiv","id":"2604.19671","version":2},"attestation_state":"computed","paper":{"title":"Linear response for Sinai billiards with small holes","license":"http://creativecommons.org/licenses/by/4.0/","headline":"The conditional survival probability measure for a Sinai billiard with a small boundary hole is differentiable at zero hole size, with an explicit derivative.","cross_cats":[],"primary_cat":"math.DS","authors_text":"Giovanni Canestrari","submitted_at":"2026-04-21T16:51:52Z","abstract_excerpt":"We show that the conditional survival probability measure for a Sinai billiard with a small hole on the boundary of the table is differentiable with respect to the size t of the hole at t = 0 and we compute the derivative."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2604.19671","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DS","submitted_at":"2026-04-21T16:51:52Z","cross_cats_sorted":[],"title_canon_sha256":"da90617b048a85a628ddc0983343e10a0c737a18225406710a2b046f16137d40","abstract_canon_sha256":"40b7452f64f2557fd793ace39ad333e4768a5125c1976ba741564a3d81fc22b4"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-25T02:01:20.793955Z","signature_b64":"GqImqexuat1ttcgBL9MBCSVidZ9VNcRYbun+zqbuZc4mgTR/lY6gfzJTZ7fOHK0VraMDx32X+VWJIKXRW2z5BQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3d91237b7aa4db9bb5957cef545b4ed4d49d8499dbb5fbbfbe44eed085398260","last_reissued_at":"2026-05-25T02:01:20.793443Z","signature_status":"signed_v1","first_computed_at":"2026-05-25T02:01:20.793443Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Linear response for Sinai billiards with small holes","license":"http://creativecommons.org/licenses/by/4.0/","headline":"The conditional survival probability measure for a Sinai billiard with a small boundary hole is differentiable at zero hole size, with an explicit derivative.","cross_cats":[],"primary_cat":"math.DS","authors_text":"Giovanni Canestrari","submitted_at":"2026-04-21T16:51:52Z","abstract_excerpt":"We show that the conditional survival probability measure for a Sinai billiard with a small hole on the boundary of the table is differentiable with respect to the size t of the hole at t = 0 and we compute the derivative."},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"We show that the conditional survival probability measure for a Sinai billiard with a small hole on the boundary of the table is differentiable with respect to the size t of the hole at t = 0 and we compute the derivative.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The Sinai billiard satisfies the standard hyperbolicity, ergodicity, and mixing properties needed for the conditional survival probability measure to exist and for linear response techniques to apply at the zero-hole limit.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"The conditional survival probability measure for a Sinai billiard with a small hole is differentiable with respect to hole size at zero, and the derivative is computed.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"The conditional survival probability measure for a Sinai billiard with a small boundary hole is differentiable at zero hole size, with an explicit derivative.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"9e1f24cd4d8e3d471bbf53aa24e53d9ae5773a3d8d3a786d1c0ebe9946f0c003"},"source":{"id":"2604.19671","kind":"arxiv","version":2},"verdict":{"id":"8271726a-efe2-4126-a564-fbbdde015da0","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-10T01:09:22.081180Z","strongest_claim":"We show that the conditional survival probability measure for a Sinai billiard with a small hole on the boundary of the table is differentiable with respect to the size t of the hole at t = 0 and we compute the derivative.","one_line_summary":"The conditional survival probability measure for a Sinai billiard with a small hole is differentiable with respect to hole size at zero, and the derivative is computed.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The Sinai billiard satisfies the standard hyperbolicity, ergodicity, and mixing properties needed for the conditional survival probability measure to exist and for linear response techniques to apply at the zero-hole limit.","pith_extraction_headline":"The conditional survival probability measure for a Sinai billiard with a small boundary hole is differentiable at zero hole size, with an explicit derivative."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2604.19671/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"ai_meta_artifact","ran_at":"2026-05-21T16:34:07.670727Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_compliance","ran_at":"2026-05-20T02:40:23.941007Z","status":"completed","version":"1.0.0","findings_count":0}],"snapshot_sha256":"e76841fc3122d095d6499cdfe7d5dfd2b01fe2f320c5462814ed5734d97a77f6"},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2604.19671","created_at":"2026-05-25T02:01:20.793521+00:00"},{"alias_kind":"arxiv_version","alias_value":"2604.19671v2","created_at":"2026-05-25T02:01:20.793521+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2604.19671","created_at":"2026-05-25T02:01:20.793521+00:00"},{"alias_kind":"pith_short_12","alias_value":"HWISG632UTNZ","created_at":"2026-05-25T02:01:20.793521+00:00"},{"alias_kind":"pith_short_16","alias_value":"HWISG632UTNZXNMV","created_at":"2026-05-25T02:01:20.793521+00:00"},{"alias_kind":"pith_short_8","alias_value":"HWISG632","created_at":"2026-05-25T02:01:20.793521+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/HWISG632UTNZXNMVPTXVIW2O2T","json":"https://pith.science/pith/HWISG632UTNZXNMVPTXVIW2O2T.json","graph_json":"https://pith.science/api/pith-number/HWISG632UTNZXNMVPTXVIW2O2T/graph.json","events_json":"https://pith.science/api/pith-number/HWISG632UTNZXNMVPTXVIW2O2T/events.json","paper":"https://pith.science/paper/HWISG632"},"agent_actions":{"view_html":"https://pith.science/pith/HWISG632UTNZXNMVPTXVIW2O2T","download_json":"https://pith.science/pith/HWISG632UTNZXNMVPTXVIW2O2T.json","view_paper":"https://pith.science/paper/HWISG632","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2604.19671&json=true","fetch_graph":"https://pith.science/api/pith-number/HWISG632UTNZXNMVPTXVIW2O2T/graph.json","fetch_events":"https://pith.science/api/pith-number/HWISG632UTNZXNMVPTXVIW2O2T/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/HWISG632UTNZXNMVPTXVIW2O2T/action/timestamp_anchor","attest_storage":"https://pith.science/pith/HWISG632UTNZXNMVPTXVIW2O2T/action/storage_attestation","attest_author":"https://pith.science/pith/HWISG632UTNZXNMVPTXVIW2O2T/action/author_attestation","sign_citation":"https://pith.science/pith/HWISG632UTNZXNMVPTXVIW2O2T/action/citation_signature","submit_replication":"https://pith.science/pith/HWISG632UTNZXNMVPTXVIW2O2T/action/replication_record"}},"created_at":"2026-05-25T02:01:20.793521+00:00","updated_at":"2026-05-25T02:01:20.793521+00:00"}