{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:U44NKJRPQUJLBPCST73V6E6ABW","short_pith_number":"pith:U44NKJRP","canonical_record":{"source":{"id":"1805.07247","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2018-05-18T14:41:02Z","cross_cats_sorted":["hep-th","math.MP"],"title_canon_sha256":"a01898b36b9bf735f713d5cd982c65b5ae5258860f790fff7059527c0e998468","abstract_canon_sha256":"9a682a7cbb49c9174719bffb7da7add2c2058c4b086eee92560968bf9f8eb13b"},"schema_version":"1.0"},"canonical_sha256":"a738d5262f8512b0bc529ff75f13c00dbd19e25beb2c49e1787420dcc53a12ed","source":{"kind":"arxiv","id":"1805.07247","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1805.07247","created_at":"2026-05-18T00:06:55Z"},{"alias_kind":"arxiv_version","alias_value":"1805.07247v3","created_at":"2026-05-18T00:06:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1805.07247","created_at":"2026-05-18T00:06:55Z"},{"alias_kind":"pith_short_12","alias_value":"U44NKJRPQUJL","created_at":"2026-05-18T12:32:56Z"},{"alias_kind":"pith_short_16","alias_value":"U44NKJRPQUJLBPCS","created_at":"2026-05-18T12:32:56Z"},{"alias_kind":"pith_short_8","alias_value":"U44NKJRP","created_at":"2026-05-18T12:32:56Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:U44NKJRPQUJLBPCST73V6E6ABW","target":"record","payload":{"canonical_record":{"source":{"id":"1805.07247","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2018-05-18T14:41:02Z","cross_cats_sorted":["hep-th","math.MP"],"title_canon_sha256":"a01898b36b9bf735f713d5cd982c65b5ae5258860f790fff7059527c0e998468","abstract_canon_sha256":"9a682a7cbb49c9174719bffb7da7add2c2058c4b086eee92560968bf9f8eb13b"},"schema_version":"1.0"},"canonical_sha256":"a738d5262f8512b0bc529ff75f13c00dbd19e25beb2c49e1787420dcc53a12ed","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:06:55.949403Z","signature_b64":"F5Sl65PyRDaqXF/b1h0BoiB/nJ89tfPd2d/NnF+Zk9YaS4y+goXTCU7mADGNMUEG6pzj/vUDHtnkUZ65BGEVBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a738d5262f8512b0bc529ff75f13c00dbd19e25beb2c49e1787420dcc53a12ed","last_reissued_at":"2026-05-18T00:06:55.948693Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:06:55.948693Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1805.07247","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:06:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/b2rp4xjPLRgAzDp3tx8ZWFGMyzkRs+wYDZHbOuHdvf5jVsmVxi12Jx/wEBg9vyPmEXPp21FGPgjrRsAXA5ZBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T08:24:47.040662Z"},"content_sha256":"9f28bf465afb3ff7505a2bf5d05cfcfb428811b9460789275693c0f5361e8fb6","schema_version":"1.0","event_id":"sha256:9f28bf465afb3ff7505a2bf5d05cfcfb428811b9460789275693c0f5361e8fb6"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:U44NKJRPQUJLBPCST73V6E6ABW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Notes about a combinatorial expression of the fundamental second kind differential on an algebraic curve","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th","math.MP"],"primary_cat":"math-ph","authors_text":"B. Eynard","submitted_at":"2018-05-18T14:41:02Z","abstract_excerpt":"The zero locus of a bivariate polynomial $P(x,y)=0$ defines a compact Riemann surface $\\Sigma$. The fundamental second kind differential is a symmetric $1\\otimes 1$ form on $\\Sigma\\times \\Sigma$ that has a double pole at coinciding points and no other pole. As its name indicates, this is one of the most important geometric objects on a Riemann surface. Here we give a rational expression in terms of combinatorics of the Newton's polygon of $P$, involving only integer combinations of products of coefficients of $P$. Since the expression uses only combinatorics, the coefficients are in the same f"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.07247","kind":"arxiv","version":3},"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":"2026-05-18T00:06:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"F1Mr/HDLDadB0lqG1Te7VKCOjVkuA50JvyvA40R39WBGyknqHUCCMg9bNDAUm7nD1sI0AGETCjH/XPb04S5IDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T08:24:47.041330Z"},"content_sha256":"e8adc2a43d19b46a223532f235d2c3c8a0a65b5e8c7cdfe5b4353ff481bb3990","schema_version":"1.0","event_id":"sha256:e8adc2a43d19b46a223532f235d2c3c8a0a65b5e8c7cdfe5b4353ff481bb3990"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/U44NKJRPQUJLBPCST73V6E6ABW/bundle.json","state_url":"https://pith.science/pith/U44NKJRPQUJLBPCST73V6E6ABW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/U44NKJRPQUJLBPCST73V6E6ABW/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":"2026-06-01T08:24:47Z","links":{"resolver":"https://pith.science/pith/U44NKJRPQUJLBPCST73V6E6ABW","bundle":"https://pith.science/pith/U44NKJRPQUJLBPCST73V6E6ABW/bundle.json","state":"https://pith.science/pith/U44NKJRPQUJLBPCST73V6E6ABW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/U44NKJRPQUJLBPCST73V6E6ABW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:U44NKJRPQUJLBPCST73V6E6ABW","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":"9a682a7cbb49c9174719bffb7da7add2c2058c4b086eee92560968bf9f8eb13b","cross_cats_sorted":["hep-th","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2018-05-18T14:41:02Z","title_canon_sha256":"a01898b36b9bf735f713d5cd982c65b5ae5258860f790fff7059527c0e998468"},"schema_version":"1.0","source":{"id":"1805.07247","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1805.07247","created_at":"2026-05-18T00:06:55Z"},{"alias_kind":"arxiv_version","alias_value":"1805.07247v3","created_at":"2026-05-18T00:06:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1805.07247","created_at":"2026-05-18T00:06:55Z"},{"alias_kind":"pith_short_12","alias_value":"U44NKJRPQUJL","created_at":"2026-05-18T12:32:56Z"},{"alias_kind":"pith_short_16","alias_value":"U44NKJRPQUJLBPCS","created_at":"2026-05-18T12:32:56Z"},{"alias_kind":"pith_short_8","alias_value":"U44NKJRP","created_at":"2026-05-18T12:32:56Z"}],"graph_snapshots":[{"event_id":"sha256:e8adc2a43d19b46a223532f235d2c3c8a0a65b5e8c7cdfe5b4353ff481bb3990","target":"graph","created_at":"2026-05-18T00:06:55Z","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":"The zero locus of a bivariate polynomial $P(x,y)=0$ defines a compact Riemann surface $\\Sigma$. The fundamental second kind differential is a symmetric $1\\otimes 1$ form on $\\Sigma\\times \\Sigma$ that has a double pole at coinciding points and no other pole. As its name indicates, this is one of the most important geometric objects on a Riemann surface. Here we give a rational expression in terms of combinatorics of the Newton's polygon of $P$, involving only integer combinations of products of coefficients of $P$. Since the expression uses only combinatorics, the coefficients are in the same f","authors_text":"B. Eynard","cross_cats":["hep-th","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2018-05-18T14:41:02Z","title":"Notes about a combinatorial expression of the fundamental second kind differential on an algebraic curve"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.07247","kind":"arxiv","version":3},"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":"sha256:9f28bf465afb3ff7505a2bf5d05cfcfb428811b9460789275693c0f5361e8fb6","target":"record","created_at":"2026-05-18T00:06:55Z","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":"9a682a7cbb49c9174719bffb7da7add2c2058c4b086eee92560968bf9f8eb13b","cross_cats_sorted":["hep-th","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2018-05-18T14:41:02Z","title_canon_sha256":"a01898b36b9bf735f713d5cd982c65b5ae5258860f790fff7059527c0e998468"},"schema_version":"1.0","source":{"id":"1805.07247","kind":"arxiv","version":3}},"canonical_sha256":"a738d5262f8512b0bc529ff75f13c00dbd19e25beb2c49e1787420dcc53a12ed","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a738d5262f8512b0bc529ff75f13c00dbd19e25beb2c49e1787420dcc53a12ed","first_computed_at":"2026-05-18T00:06:55.948693Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:06:55.948693Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"F5Sl65PyRDaqXF/b1h0BoiB/nJ89tfPd2d/NnF+Zk9YaS4y+goXTCU7mADGNMUEG6pzj/vUDHtnkUZ65BGEVBA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:06:55.949403Z","signed_message":"canonical_sha256_bytes"},"source_id":"1805.07247","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9f28bf465afb3ff7505a2bf5d05cfcfb428811b9460789275693c0f5361e8fb6","sha256:e8adc2a43d19b46a223532f235d2c3c8a0a65b5e8c7cdfe5b4353ff481bb3990"],"state_sha256":"95fdac652318eda1f7018c8839dac8f41de7d28b465ccd44e74e77af15e9d6bb"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6xRu3adsHaC/jMePB9CZVHA8HKmJj3obkekK4GaLzEjkx7Abj1c1KEZLgEiBSihefaNl/k1XQYZRL0LZVjYiCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T08:24:47.044474Z","bundle_sha256":"cd879cbf5a072b42dd7f130a13dce74240029fcdfaaa8826de19c421eaec2f9c"}}