{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:CJL7OJ5YAHD6647BBU2XW5TUXA","short_pith_number":"pith:CJL7OJ5Y","canonical_record":{"source":{"id":"1401.5736","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2014-01-22T17:23:47Z","cross_cats_sorted":["math.DS"],"title_canon_sha256":"f8cd16ac3d1846720f669b2d9b2a841aa75b191231723faa8e61199e22d9bb8e","abstract_canon_sha256":"b91542563c1b58e2708b72889346a188ea15f8e843e2da79145261d4475bd201"},"schema_version":"1.0"},"canonical_sha256":"1257f727b801c7ef73e10d357b7674b81d0fa628cc6b3e3863f4f6a2411b2017","source":{"kind":"arxiv","id":"1401.5736","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1401.5736","created_at":"2026-05-18T02:52:57Z"},{"alias_kind":"arxiv_version","alias_value":"1401.5736v4","created_at":"2026-05-18T02:52:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1401.5736","created_at":"2026-05-18T02:52:57Z"},{"alias_kind":"pith_short_12","alias_value":"CJL7OJ5YAHD6","created_at":"2026-05-18T12:28:22Z"},{"alias_kind":"pith_short_16","alias_value":"CJL7OJ5YAHD6647B","created_at":"2026-05-18T12:28:22Z"},{"alias_kind":"pith_short_8","alias_value":"CJL7OJ5Y","created_at":"2026-05-18T12:28:22Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:CJL7OJ5YAHD6647BBU2XW5TUXA","target":"record","payload":{"canonical_record":{"source":{"id":"1401.5736","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2014-01-22T17:23:47Z","cross_cats_sorted":["math.DS"],"title_canon_sha256":"f8cd16ac3d1846720f669b2d9b2a841aa75b191231723faa8e61199e22d9bb8e","abstract_canon_sha256":"b91542563c1b58e2708b72889346a188ea15f8e843e2da79145261d4475bd201"},"schema_version":"1.0"},"canonical_sha256":"1257f727b801c7ef73e10d357b7674b81d0fa628cc6b3e3863f4f6a2411b2017","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:52:57.861830Z","signature_b64":"/wBhmZGwZ+I8Zr2j/sEaGzu8qY4+cxvZXwaIvg0/WLzLzj7SMRjZXLhAwNCKRgRnEjm+gna6XTgoVv68ou5vCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1257f727b801c7ef73e10d357b7674b81d0fa628cc6b3e3863f4f6a2411b2017","last_reissued_at":"2026-05-18T02:52:57.861295Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:52:57.861295Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1401.5736","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:52:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/A6IcE1i8asJLQg3KaaxOHSkeZ++ApQTjRWGoXYAvAVMiRNVwsgShiwdyGasAC+f2Cpsy6HlvwsLfKp8zcFlBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-24T17:27:55.836162Z"},"content_sha256":"8028a947d36c8cca9b9624c74f96b57dc087478c0d5abf40cfee0778c5c58a01","schema_version":"1.0","event_id":"sha256:8028a947d36c8cca9b9624c74f96b57dc087478c0d5abf40cfee0778c5c58a01"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:CJL7OJ5YAHD6647BBU2XW5TUXA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Statistics of Random 3-Manifolds occasionally fibering over the circle","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.GT","authors_text":"Igor Rivin","submitted_at":"2014-01-22T17:23:47Z","abstract_excerpt":"We study random elements of subgroups (and cosets) of the mapping class group of a closed hyperbolic surface, in part through the properties of their mapping tori. In particular, we study the distribution of the homology of the mapping torus (with rational, integer, and finite field coefficients, the hyperbolic volume (whenever the manifold is hyperbolic), the dilatation of the monodromy, the injectivity radius, and the bottom eigenvalue of the Laplacian on these mapping tori. We also study mapping tori of punctured surface bundles, and various invariants of their Dehn fillings. We also study "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.5736","kind":"arxiv","version":4},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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":"2026-05-18T02:52:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LnapLKT1sZRosYMM6/Tb7y1Oiys1GuHWhUqv+drBZmPspR1PggXmOvVa802V/luw5EjSwwO3kpfZobNWlxrnBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-24T17:27:55.836910Z"},"content_sha256":"39c20aae51f287dc35fe24cda2fd6bc71be85dea05fd6c9a507086122a8de99f","schema_version":"1.0","event_id":"sha256:39c20aae51f287dc35fe24cda2fd6bc71be85dea05fd6c9a507086122a8de99f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/CJL7OJ5YAHD6647BBU2XW5TUXA/bundle.json","state_url":"https://pith.science/pith/CJL7OJ5YAHD6647BBU2XW5TUXA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/CJL7OJ5YAHD6647BBU2XW5TUXA/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":"2026-05-24T17:27:55Z","links":{"resolver":"https://pith.science/pith/CJL7OJ5YAHD6647BBU2XW5TUXA","bundle":"https://pith.science/pith/CJL7OJ5YAHD6647BBU2XW5TUXA/bundle.json","state":"https://pith.science/pith/CJL7OJ5YAHD6647BBU2XW5TUXA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/CJL7OJ5YAHD6647BBU2XW5TUXA/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:CJL7OJ5YAHD6647BBU2XW5TUXA","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":"b91542563c1b58e2708b72889346a188ea15f8e843e2da79145261d4475bd201","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2014-01-22T17:23:47Z","title_canon_sha256":"f8cd16ac3d1846720f669b2d9b2a841aa75b191231723faa8e61199e22d9bb8e"},"schema_version":"1.0","source":{"id":"1401.5736","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1401.5736","created_at":"2026-05-18T02:52:57Z"},{"alias_kind":"arxiv_version","alias_value":"1401.5736v4","created_at":"2026-05-18T02:52:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1401.5736","created_at":"2026-05-18T02:52:57Z"},{"alias_kind":"pith_short_12","alias_value":"CJL7OJ5YAHD6","created_at":"2026-05-18T12:28:22Z"},{"alias_kind":"pith_short_16","alias_value":"CJL7OJ5YAHD6647B","created_at":"2026-05-18T12:28:22Z"},{"alias_kind":"pith_short_8","alias_value":"CJL7OJ5Y","created_at":"2026-05-18T12:28:22Z"}],"graph_snapshots":[{"event_id":"sha256:39c20aae51f287dc35fe24cda2fd6bc71be85dea05fd6c9a507086122a8de99f","target":"graph","created_at":"2026-05-18T02:52:57Z","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"},"paper":{"abstract_excerpt":"We study random elements of subgroups (and cosets) of the mapping class group of a closed hyperbolic surface, in part through the properties of their mapping tori. In particular, we study the distribution of the homology of the mapping torus (with rational, integer, and finite field coefficients, the hyperbolic volume (whenever the manifold is hyperbolic), the dilatation of the monodromy, the injectivity radius, and the bottom eigenvalue of the Laplacian on these mapping tori. We also study mapping tori of punctured surface bundles, and various invariants of their Dehn fillings. We also study ","authors_text":"Igor Rivin","cross_cats":["math.DS"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2014-01-22T17:23:47Z","title":"Statistics of Random 3-Manifolds occasionally fibering over the circle"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.5736","kind":"arxiv","version":4},"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":"sha256:8028a947d36c8cca9b9624c74f96b57dc087478c0d5abf40cfee0778c5c58a01","target":"record","created_at":"2026-05-18T02:52:57Z","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":"b91542563c1b58e2708b72889346a188ea15f8e843e2da79145261d4475bd201","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2014-01-22T17:23:47Z","title_canon_sha256":"f8cd16ac3d1846720f669b2d9b2a841aa75b191231723faa8e61199e22d9bb8e"},"schema_version":"1.0","source":{"id":"1401.5736","kind":"arxiv","version":4}},"canonical_sha256":"1257f727b801c7ef73e10d357b7674b81d0fa628cc6b3e3863f4f6a2411b2017","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1257f727b801c7ef73e10d357b7674b81d0fa628cc6b3e3863f4f6a2411b2017","first_computed_at":"2026-05-18T02:52:57.861295Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:52:57.861295Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"/wBhmZGwZ+I8Zr2j/sEaGzu8qY4+cxvZXwaIvg0/WLzLzj7SMRjZXLhAwNCKRgRnEjm+gna6XTgoVv68ou5vCg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:52:57.861830Z","signed_message":"canonical_sha256_bytes"},"source_id":"1401.5736","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8028a947d36c8cca9b9624c74f96b57dc087478c0d5abf40cfee0778c5c58a01","sha256:39c20aae51f287dc35fe24cda2fd6bc71be85dea05fd6c9a507086122a8de99f"],"state_sha256":"d0bba73fc7b4f8b86e81f227cdf4719d65dd349895cff14723bd50c6a7e7035d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JZGZowakL1nlE+YsDuB6L5kX1cCMibM3+/uyh6AGRsvLfcBNncj3Un0jnr9kPQfePLWe9nfjOwLwOTOiZ4oKDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-24T17:27:55.841237Z","bundle_sha256":"1dd9f84c3fe120caf87b1e768eb19c1e662843855a51403e9b27843cc3dfe1eb"}}