{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:2GV4YXUYUMDYKWNHPD5DBZ6G3K","short_pith_number":"pith:2GV4YXUY","canonical_record":{"source":{"id":"1504.01186","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2015-04-06T02:08:30Z","cross_cats_sorted":["math.AG","math.MP","math.QA","nlin.SI"],"title_canon_sha256":"dcd2317510fb41358fb1a94fbd0274a9e018d0d744c2152878214e9824d50260","abstract_canon_sha256":"52fa640ce79f78d8527c757394a93131a89bd6d59e03fa41a71dfcf25e80b62a"},"schema_version":"1.0"},"canonical_sha256":"d1abcc5e98a3078559a778fa30e7c6daa6df4b1bf672e75b73655397a7f59972","source":{"kind":"arxiv","id":"1504.01186","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1504.01186","created_at":"2026-05-18T02:19:34Z"},{"alias_kind":"arxiv_version","alias_value":"1504.01186v1","created_at":"2026-05-18T02:19:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.01186","created_at":"2026-05-18T02:19:34Z"},{"alias_kind":"pith_short_12","alias_value":"2GV4YXUYUMDY","created_at":"2026-05-18T12:28:59Z"},{"alias_kind":"pith_short_16","alias_value":"2GV4YXUYUMDYKWNH","created_at":"2026-05-18T12:28:59Z"},{"alias_kind":"pith_short_8","alias_value":"2GV4YXUY","created_at":"2026-05-18T12:28:59Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:2GV4YXUYUMDYKWNHPD5DBZ6G3K","target":"record","payload":{"canonical_record":{"source":{"id":"1504.01186","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2015-04-06T02:08:30Z","cross_cats_sorted":["math.AG","math.MP","math.QA","nlin.SI"],"title_canon_sha256":"dcd2317510fb41358fb1a94fbd0274a9e018d0d744c2152878214e9824d50260","abstract_canon_sha256":"52fa640ce79f78d8527c757394a93131a89bd6d59e03fa41a71dfcf25e80b62a"},"schema_version":"1.0"},"canonical_sha256":"d1abcc5e98a3078559a778fa30e7c6daa6df4b1bf672e75b73655397a7f59972","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:19:34.961741Z","signature_b64":"TZjzmZezkvX97gM84z66xvfiS3vLMHby47N1cEVDbnEy2NK2EButML4SjjKYGcTb7x2TSQz+RWSPQZVnq664Bw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d1abcc5e98a3078559a778fa30e7c6daa6df4b1bf672e75b73655397a7f59972","last_reissued_at":"2026-05-18T02:19:34.961079Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:19:34.961079Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1504.01186","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:19:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RwmoQu92fYorN4RyTE3Rv0iB2/vRPNMsG5jB95/V3dIqzjCGdUhzg2YjVyqzmQvzgkD6N4nyKUWUXi3KGHnRDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T11:06:50.995937Z"},"content_sha256":"8a2a8b736f81003df412d20a7c1f4af0c6911373936ff24a35390bdfc168466f","schema_version":"1.0","event_id":"sha256:8a2a8b736f81003df412d20a7c1f4af0c6911373936ff24a35390bdfc168466f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:2GV4YXUYUMDYKWNHPD5DBZ6G3K","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Tau Function Approach to Theta Functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG","math.MP","math.QA","nlin.SI"],"primary_cat":"math-ph","authors_text":"Atsushi Nakayashiki","submitted_at":"2015-04-06T02:08:30Z","abstract_excerpt":"We study theta functions of a Riemann surface of genus g from the view point of tau function of a hierarchy of soliton equations. We study two kinds of series expansions. One is the Taylor expansion at any point of the theta divisor. We describe the initial term of the expansion by the Schur function corresponding to the partition determined by the gap sequence of a certain flat line bundle. The other is the expansion of the theta function and its certain derivatives in one of the variables on the Abel-Jacobi images of k points on a Riemann surface with k less than or equal to g. We determine "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.01186","kind":"arxiv","version":1},"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":"2026-05-18T02:19:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mtjZCcZFfqYZPzQ1x6xIAPVTyaSSPfq1GSm/4IREttSRz5Tn+MZblcj9jd7QT01P+ypICeYDWT/DN5NR0GokCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T11:06:50.996291Z"},"content_sha256":"ebe092df067da5634acdf33fae5d0218f2cb0006bd61d4113717288adbc18ad8","schema_version":"1.0","event_id":"sha256:ebe092df067da5634acdf33fae5d0218f2cb0006bd61d4113717288adbc18ad8"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/2GV4YXUYUMDYKWNHPD5DBZ6G3K/bundle.json","state_url":"https://pith.science/pith/2GV4YXUYUMDYKWNHPD5DBZ6G3K/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/2GV4YXUYUMDYKWNHPD5DBZ6G3K/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":"2026-05-28T11:06:50Z","links":{"resolver":"https://pith.science/pith/2GV4YXUYUMDYKWNHPD5DBZ6G3K","bundle":"https://pith.science/pith/2GV4YXUYUMDYKWNHPD5DBZ6G3K/bundle.json","state":"https://pith.science/pith/2GV4YXUYUMDYKWNHPD5DBZ6G3K/state.json","well_known_bundle":"https://pith.science/.well-known/pith/2GV4YXUYUMDYKWNHPD5DBZ6G3K/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:2GV4YXUYUMDYKWNHPD5DBZ6G3K","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":"52fa640ce79f78d8527c757394a93131a89bd6d59e03fa41a71dfcf25e80b62a","cross_cats_sorted":["math.AG","math.MP","math.QA","nlin.SI"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2015-04-06T02:08:30Z","title_canon_sha256":"dcd2317510fb41358fb1a94fbd0274a9e018d0d744c2152878214e9824d50260"},"schema_version":"1.0","source":{"id":"1504.01186","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1504.01186","created_at":"2026-05-18T02:19:34Z"},{"alias_kind":"arxiv_version","alias_value":"1504.01186v1","created_at":"2026-05-18T02:19:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.01186","created_at":"2026-05-18T02:19:34Z"},{"alias_kind":"pith_short_12","alias_value":"2GV4YXUYUMDY","created_at":"2026-05-18T12:28:59Z"},{"alias_kind":"pith_short_16","alias_value":"2GV4YXUYUMDYKWNH","created_at":"2026-05-18T12:28:59Z"},{"alias_kind":"pith_short_8","alias_value":"2GV4YXUY","created_at":"2026-05-18T12:28:59Z"}],"graph_snapshots":[{"event_id":"sha256:ebe092df067da5634acdf33fae5d0218f2cb0006bd61d4113717288adbc18ad8","target":"graph","created_at":"2026-05-18T02:19:34Z","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 theta functions of a Riemann surface of genus g from the view point of tau function of a hierarchy of soliton equations. We study two kinds of series expansions. One is the Taylor expansion at any point of the theta divisor. We describe the initial term of the expansion by the Schur function corresponding to the partition determined by the gap sequence of a certain flat line bundle. The other is the expansion of the theta function and its certain derivatives in one of the variables on the Abel-Jacobi images of k points on a Riemann surface with k less than or equal to g. We determine ","authors_text":"Atsushi Nakayashiki","cross_cats":["math.AG","math.MP","math.QA","nlin.SI"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2015-04-06T02:08:30Z","title":"Tau Function Approach to Theta Functions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.01186","kind":"arxiv","version":1},"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":"sha256:8a2a8b736f81003df412d20a7c1f4af0c6911373936ff24a35390bdfc168466f","target":"record","created_at":"2026-05-18T02:19:34Z","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":"52fa640ce79f78d8527c757394a93131a89bd6d59e03fa41a71dfcf25e80b62a","cross_cats_sorted":["math.AG","math.MP","math.QA","nlin.SI"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2015-04-06T02:08:30Z","title_canon_sha256":"dcd2317510fb41358fb1a94fbd0274a9e018d0d744c2152878214e9824d50260"},"schema_version":"1.0","source":{"id":"1504.01186","kind":"arxiv","version":1}},"canonical_sha256":"d1abcc5e98a3078559a778fa30e7c6daa6df4b1bf672e75b73655397a7f59972","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d1abcc5e98a3078559a778fa30e7c6daa6df4b1bf672e75b73655397a7f59972","first_computed_at":"2026-05-18T02:19:34.961079Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:19:34.961079Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"TZjzmZezkvX97gM84z66xvfiS3vLMHby47N1cEVDbnEy2NK2EButML4SjjKYGcTb7x2TSQz+RWSPQZVnq664Bw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:19:34.961741Z","signed_message":"canonical_sha256_bytes"},"source_id":"1504.01186","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8a2a8b736f81003df412d20a7c1f4af0c6911373936ff24a35390bdfc168466f","sha256:ebe092df067da5634acdf33fae5d0218f2cb0006bd61d4113717288adbc18ad8"],"state_sha256":"b3393870d125e570472bd439eae06f304dff92930e18cc27008482015a75d824"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"eqg64VX86v5zFUCOFa9UTQbh3tt5X4/7ftwASdgB08ym6Dz/eKdNOhv6o3+Yuwh2WR/krfdvmcTjq/f5fN5YCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T11:06:50.998232Z","bundle_sha256":"bf14ab69403e579d75bf3ce7d9a821788188e5e3d4f19de70cf845a2625006bc"}}