{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:XEV5ZPFQWJVIWV5I7VNGI4VZ2M","short_pith_number":"pith:XEV5ZPFQ","canonical_record":{"source":{"id":"1212.1714","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2012-12-07T17:12:10Z","cross_cats_sorted":["math.CO","math.DS"],"title_canon_sha256":"62599c4a5da3d340596fdd5b26fbf5babdcfb8084047f9c2c10b141ed5268bfa","abstract_canon_sha256":"8e555f5353872b76c8757aee1e0ce25a368f094e5dba55146ac80895c027f511"},"schema_version":"1.0"},"canonical_sha256":"b92bdcbcb0b26a8b57a8fd5a6472b9d3311b03466fb461c5430e84e1fe7de6c5","source":{"kind":"arxiv","id":"1212.1714","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1212.1714","created_at":"2026-05-18T02:48:17Z"},{"alias_kind":"arxiv_version","alias_value":"1212.1714v4","created_at":"2026-05-18T02:48:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1212.1714","created_at":"2026-05-18T02:48:17Z"},{"alias_kind":"pith_short_12","alias_value":"XEV5ZPFQWJVI","created_at":"2026-05-18T12:27:27Z"},{"alias_kind":"pith_short_16","alias_value":"XEV5ZPFQWJVIWV5I","created_at":"2026-05-18T12:27:27Z"},{"alias_kind":"pith_short_8","alias_value":"XEV5ZPFQ","created_at":"2026-05-18T12:27:27Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:XEV5ZPFQWJVIWV5I7VNGI4VZ2M","target":"record","payload":{"canonical_record":{"source":{"id":"1212.1714","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2012-12-07T17:12:10Z","cross_cats_sorted":["math.CO","math.DS"],"title_canon_sha256":"62599c4a5da3d340596fdd5b26fbf5babdcfb8084047f9c2c10b141ed5268bfa","abstract_canon_sha256":"8e555f5353872b76c8757aee1e0ce25a368f094e5dba55146ac80895c027f511"},"schema_version":"1.0"},"canonical_sha256":"b92bdcbcb0b26a8b57a8fd5a6472b9d3311b03466fb461c5430e84e1fe7de6c5","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:48:17.906642Z","signature_b64":"TUZzCMw0g/4ukRpNLbc6GaoKnA/ZAe6vWArGz0johzl9jL3TqFPheagGHVHeknifEvWGmNAwiaxPKDVzs+LdBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b92bdcbcb0b26a8b57a8fd5a6472b9d3311b03466fb461c5430e84e1fe7de6c5","last_reissued_at":"2026-05-18T02:48:17.906157Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:48:17.906157Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1212.1714","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":"2026-05-18T02:48:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ipd4/ucmJQKk6xvdC83oHGP/i2qAouYuO7xO2xR20+oKKLB7Cnr817yyiQppkfkdqQt8o3FsAO/PhteIYb91CQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T07:54:40.919377Z"},"content_sha256":"659e3843e873600bb8d780c9d1644c2e4769009841ad19912a8832ebda82bd8f","schema_version":"1.0","event_id":"sha256:659e3843e873600bb8d780c9d1644c2e4769009841ad19912a8832ebda82bd8f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:XEV5ZPFQWJVIWV5I7VNGI4VZ2M","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Counting generalized Jenkins-Strebel differentials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO","math.DS"],"primary_cat":"math.GT","authors_text":"Alex Eskin, Anton Zorich, Jayadev S. Athreya","submitted_at":"2012-12-07T17:12:10Z","abstract_excerpt":"We study the combinatorial geometry of \"lattice\" Jenkins--Strebel differentials with simple zeroes and simple poles on $\\mathbb{C}P^1$ and of the corresponding counting functions. Developing the results of M. Kontsevich we evaluate the leading term of the symmetric polynomial counting the number of such \"lattice\" Jenkins-Strebel differentials having all zeroes on a single singular layer. This allows us to express the number of general \"lattice\" Jenkins-Strebel differentials as an appropriate weighted sum over decorated trees.\n  The problem of counting Jenkins-Strebel differentials is equivalen"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.1714","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":"2026-05-18T02:48:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xGN2qWM83VZbfOBdRQ5Kg4NuSsoLzLwtKsNeqaMR8GFAakA7JRa2XmEw4xH9Ma3+y6H8+AN7kaoHKDnR5QYACQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T07:54:40.919728Z"},"content_sha256":"7605d1117f8beff251625f7ca4647050a63fa0432451df3ff07aaeabf4c19784","schema_version":"1.0","event_id":"sha256:7605d1117f8beff251625f7ca4647050a63fa0432451df3ff07aaeabf4c19784"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/XEV5ZPFQWJVIWV5I7VNGI4VZ2M/bundle.json","state_url":"https://pith.science/pith/XEV5ZPFQWJVIWV5I7VNGI4VZ2M/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/XEV5ZPFQWJVIWV5I7VNGI4VZ2M/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":"2026-06-01T07:54:40Z","links":{"resolver":"https://pith.science/pith/XEV5ZPFQWJVIWV5I7VNGI4VZ2M","bundle":"https://pith.science/pith/XEV5ZPFQWJVIWV5I7VNGI4VZ2M/bundle.json","state":"https://pith.science/pith/XEV5ZPFQWJVIWV5I7VNGI4VZ2M/state.json","well_known_bundle":"https://pith.science/.well-known/pith/XEV5ZPFQWJVIWV5I7VNGI4VZ2M/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:XEV5ZPFQWJVIWV5I7VNGI4VZ2M","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":"8e555f5353872b76c8757aee1e0ce25a368f094e5dba55146ac80895c027f511","cross_cats_sorted":["math.CO","math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2012-12-07T17:12:10Z","title_canon_sha256":"62599c4a5da3d340596fdd5b26fbf5babdcfb8084047f9c2c10b141ed5268bfa"},"schema_version":"1.0","source":{"id":"1212.1714","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1212.1714","created_at":"2026-05-18T02:48:17Z"},{"alias_kind":"arxiv_version","alias_value":"1212.1714v4","created_at":"2026-05-18T02:48:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1212.1714","created_at":"2026-05-18T02:48:17Z"},{"alias_kind":"pith_short_12","alias_value":"XEV5ZPFQWJVI","created_at":"2026-05-18T12:27:27Z"},{"alias_kind":"pith_short_16","alias_value":"XEV5ZPFQWJVIWV5I","created_at":"2026-05-18T12:27:27Z"},{"alias_kind":"pith_short_8","alias_value":"XEV5ZPFQ","created_at":"2026-05-18T12:27:27Z"}],"graph_snapshots":[{"event_id":"sha256:7605d1117f8beff251625f7ca4647050a63fa0432451df3ff07aaeabf4c19784","target":"graph","created_at":"2026-05-18T02:48:17Z","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 the combinatorial geometry of \"lattice\" Jenkins--Strebel differentials with simple zeroes and simple poles on $\\mathbb{C}P^1$ and of the corresponding counting functions. Developing the results of M. Kontsevich we evaluate the leading term of the symmetric polynomial counting the number of such \"lattice\" Jenkins-Strebel differentials having all zeroes on a single singular layer. This allows us to express the number of general \"lattice\" Jenkins-Strebel differentials as an appropriate weighted sum over decorated trees.\n  The problem of counting Jenkins-Strebel differentials is equivalen","authors_text":"Alex Eskin, Anton Zorich, Jayadev S. Athreya","cross_cats":["math.CO","math.DS"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2012-12-07T17:12:10Z","title":"Counting generalized Jenkins-Strebel differentials"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.1714","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":"sha256:659e3843e873600bb8d780c9d1644c2e4769009841ad19912a8832ebda82bd8f","target":"record","created_at":"2026-05-18T02:48:17Z","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":"8e555f5353872b76c8757aee1e0ce25a368f094e5dba55146ac80895c027f511","cross_cats_sorted":["math.CO","math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2012-12-07T17:12:10Z","title_canon_sha256":"62599c4a5da3d340596fdd5b26fbf5babdcfb8084047f9c2c10b141ed5268bfa"},"schema_version":"1.0","source":{"id":"1212.1714","kind":"arxiv","version":4}},"canonical_sha256":"b92bdcbcb0b26a8b57a8fd5a6472b9d3311b03466fb461c5430e84e1fe7de6c5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b92bdcbcb0b26a8b57a8fd5a6472b9d3311b03466fb461c5430e84e1fe7de6c5","first_computed_at":"2026-05-18T02:48:17.906157Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:48:17.906157Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"TUZzCMw0g/4ukRpNLbc6GaoKnA/ZAe6vWArGz0johzl9jL3TqFPheagGHVHeknifEvWGmNAwiaxPKDVzs+LdBg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:48:17.906642Z","signed_message":"canonical_sha256_bytes"},"source_id":"1212.1714","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:659e3843e873600bb8d780c9d1644c2e4769009841ad19912a8832ebda82bd8f","sha256:7605d1117f8beff251625f7ca4647050a63fa0432451df3ff07aaeabf4c19784"],"state_sha256":"8bdd74b2761f495ceecc85c5236c94822f8e024291edbd519ecb9ccda9b05164"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LkmZXvHok2/cxsfO+fEelHxGvXLFb8qU0mbKZ/10LUCFjkxWo+aRSjdCVsyZXngPYIkQh5QLQ0eVsgO8BihDBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T07:54:40.921734Z","bundle_sha256":"b6124c84a36c40bafc8e9c4ba09e9aa7fcd0797f302842a5a945a131814145f1"}}