{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:V6YAEI7DJX7RR4LNCLULSDOD7E","short_pith_number":"pith:V6YAEI7D","canonical_record":{"source":{"id":"1705.05190","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2017-05-15T12:46:53Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"445e9663c8afcc24a4eea5676853bdb42a491125b2cd7f216c130455042191c5","abstract_canon_sha256":"136c690f1ace7942426bf53473dcc57808038b363e4acebf37bda57c360f288a"},"schema_version":"1.0"},"canonical_sha256":"afb00223e34dff18f16d12e8b90dc3f9395162ea8cdb9924eb163a8947a2987b","source":{"kind":"arxiv","id":"1705.05190","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1705.05190","created_at":"2026-07-05T01:43:22Z"},{"alias_kind":"arxiv_version","alias_value":"1705.05190v2","created_at":"2026-07-05T01:43:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.05190","created_at":"2026-07-05T01:43:22Z"},{"alias_kind":"pith_short_12","alias_value":"V6YAEI7DJX7R","created_at":"2026-07-05T01:43:22Z"},{"alias_kind":"pith_short_16","alias_value":"V6YAEI7DJX7RR4LN","created_at":"2026-07-05T01:43:22Z"},{"alias_kind":"pith_short_8","alias_value":"V6YAEI7D","created_at":"2026-07-05T01:43:22Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:V6YAEI7DJX7RR4LNCLULSDOD7E","target":"record","payload":{"canonical_record":{"source":{"id":"1705.05190","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2017-05-15T12:46:53Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"445e9663c8afcc24a4eea5676853bdb42a491125b2cd7f216c130455042191c5","abstract_canon_sha256":"136c690f1ace7942426bf53473dcc57808038b363e4acebf37bda57c360f288a"},"schema_version":"1.0"},"canonical_sha256":"afb00223e34dff18f16d12e8b90dc3f9395162ea8cdb9924eb163a8947a2987b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T01:43:22.366790Z","signature_b64":"XMwdmMUXC+7YMN72YE7y2XYTUTLFfAG/whgRI+rMtr1m/os0i50rq7hDo8k005IdYFyoC7eW8VL3LqJoadE9Ag==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"afb00223e34dff18f16d12e8b90dc3f9395162ea8cdb9924eb163a8947a2987b","last_reissued_at":"2026-07-05T01:43:22.366392Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T01:43:22.366392Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1705.05190","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T01:43:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EDTmFrT+TdWFTTPHy7Bz+LPyxPETCZO0KgYa026djoFFmR1URvcPGbNYoysnH+3kqaZK9/HuLmZvGn49fAMEAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-17T02:57:09.924102Z"},"content_sha256":"23da493fbc4955f025bda41c28ae937fa419597f4ce37f818b9aa6ab7fa19b62","schema_version":"1.0","event_id":"sha256:23da493fbc4955f025bda41c28ae937fa419597f4ce37f818b9aa6ab7fa19b62"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:V6YAEI7DJX7RR4LNCLULSDOD7E","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Enumeration of meanders and Masur-Veech volumes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.GT","authors_text":"Anton Zorich, Elise Goujard, Peter Zograf, Vincent Delecroix","submitted_at":"2017-05-15T12:46:53Z","abstract_excerpt":"A meander is a topological configuration of a line and a simple closed curve in the plane (or a pair of simple closed curves on the 2-sphere) intersecting transversally. Meanders can be traced back to H. Poincar\\'e and naturally appear in various areas of mathematics, theoretical physics and computational biology (in particular, they provide a model of polymer folding). Enumeration of meanders is an important open problem. The number of meanders with 2N crossings grows exponentially when N grows, but the longstanding problem on the precise asymptotics is still out of reach. We show that the si"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.05190","kind":"arxiv","version":2},"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/1705.05190/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":"2026-07-05T01:43:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ev1AVDUPiJwd4VgbkMHDYQcAAtvH/ihDzn/Rt+Zi7HpQodxFfHjFP65QQl2OWIdi3NdewrEswfMRME7DwV9lCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-17T02:57:09.924626Z"},"content_sha256":"822dd41065ab5f68497e7eb4e6e4a1e2b69231cf6a583aaf8c268241bf7f8d46","schema_version":"1.0","event_id":"sha256:822dd41065ab5f68497e7eb4e6e4a1e2b69231cf6a583aaf8c268241bf7f8d46"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/V6YAEI7DJX7RR4LNCLULSDOD7E/bundle.json","state_url":"https://pith.science/pith/V6YAEI7DJX7RR4LNCLULSDOD7E/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/V6YAEI7DJX7RR4LNCLULSDOD7E/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":"2026-08-17T02:57:09Z","links":{"resolver":"https://pith.science/pith/V6YAEI7DJX7RR4LNCLULSDOD7E","bundle":"https://pith.science/pith/V6YAEI7DJX7RR4LNCLULSDOD7E/bundle.json","state":"https://pith.science/pith/V6YAEI7DJX7RR4LNCLULSDOD7E/state.json","well_known_bundle":"https://pith.science/.well-known/pith/V6YAEI7DJX7RR4LNCLULSDOD7E/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:V6YAEI7DJX7RR4LNCLULSDOD7E","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":"136c690f1ace7942426bf53473dcc57808038b363e4acebf37bda57c360f288a","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2017-05-15T12:46:53Z","title_canon_sha256":"445e9663c8afcc24a4eea5676853bdb42a491125b2cd7f216c130455042191c5"},"schema_version":"1.0","source":{"id":"1705.05190","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1705.05190","created_at":"2026-07-05T01:43:22Z"},{"alias_kind":"arxiv_version","alias_value":"1705.05190v2","created_at":"2026-07-05T01:43:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.05190","created_at":"2026-07-05T01:43:22Z"},{"alias_kind":"pith_short_12","alias_value":"V6YAEI7DJX7R","created_at":"2026-07-05T01:43:22Z"},{"alias_kind":"pith_short_16","alias_value":"V6YAEI7DJX7RR4LN","created_at":"2026-07-05T01:43:22Z"},{"alias_kind":"pith_short_8","alias_value":"V6YAEI7D","created_at":"2026-07-05T01:43:22Z"}],"graph_snapshots":[{"event_id":"sha256:822dd41065ab5f68497e7eb4e6e4a1e2b69231cf6a583aaf8c268241bf7f8d46","target":"graph","created_at":"2026-07-05T01:43:22Z","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/1705.05190/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"A meander is a topological configuration of a line and a simple closed curve in the plane (or a pair of simple closed curves on the 2-sphere) intersecting transversally. Meanders can be traced back to H. Poincar\\'e and naturally appear in various areas of mathematics, theoretical physics and computational biology (in particular, they provide a model of polymer folding). Enumeration of meanders is an important open problem. The number of meanders with 2N crossings grows exponentially when N grows, but the longstanding problem on the precise asymptotics is still out of reach. We show that the si","authors_text":"Anton Zorich, Elise Goujard, Peter Zograf, Vincent Delecroix","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2017-05-15T12:46:53Z","title":"Enumeration of meanders and Masur-Veech volumes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.05190","kind":"arxiv","version":2},"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":"sha256:23da493fbc4955f025bda41c28ae937fa419597f4ce37f818b9aa6ab7fa19b62","target":"record","created_at":"2026-07-05T01:43:22Z","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":"136c690f1ace7942426bf53473dcc57808038b363e4acebf37bda57c360f288a","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2017-05-15T12:46:53Z","title_canon_sha256":"445e9663c8afcc24a4eea5676853bdb42a491125b2cd7f216c130455042191c5"},"schema_version":"1.0","source":{"id":"1705.05190","kind":"arxiv","version":2}},"canonical_sha256":"afb00223e34dff18f16d12e8b90dc3f9395162ea8cdb9924eb163a8947a2987b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"afb00223e34dff18f16d12e8b90dc3f9395162ea8cdb9924eb163a8947a2987b","first_computed_at":"2026-07-05T01:43:22.366392Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T01:43:22.366392Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"XMwdmMUXC+7YMN72YE7y2XYTUTLFfAG/whgRI+rMtr1m/os0i50rq7hDo8k005IdYFyoC7eW8VL3LqJoadE9Ag==","signature_status":"signed_v1","signed_at":"2026-07-05T01:43:22.366790Z","signed_message":"canonical_sha256_bytes"},"source_id":"1705.05190","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:23da493fbc4955f025bda41c28ae937fa419597f4ce37f818b9aa6ab7fa19b62","sha256:822dd41065ab5f68497e7eb4e6e4a1e2b69231cf6a583aaf8c268241bf7f8d46"],"state_sha256":"1e97c921c7a4988174bfe3e585632bd4da9b72d30812bd09074897bcb4413fe8"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"212ltGSG0rNLBoPemSjL23/EQTjw3c7RJfNkK3lJ3DumeyLCCF2Y3DNPAohOyQBYL+G6/6ulseRrHItgErJWBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-17T02:57:09.928054Z","bundle_sha256":"cfc3802f5e0057318019bbd12600a2c7ced943a7931546f9fa036bd72d3baf74"}}