{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2009:EZJ3LBEJ5A3E66NE2VTGEOB4KS","short_pith_number":"pith:EZJ3LBEJ","canonical_record":{"source":{"id":"0908.1197","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2009-08-08T22:13:51Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"1a0f75404733455931ba351558c909b151cc2f7ca1aef60a578dc58a17a06659","abstract_canon_sha256":"921f7d55f73b33c3aa039b2a774af8bb8b2a38890a42dd571a3f5495f25b9434"},"schema_version":"1.0"},"canonical_sha256":"2653b58489e8364f79a4d56662383c54998213961833972bc3bd344802518194","source":{"kind":"arxiv","id":"0908.1197","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0908.1197","created_at":"2026-05-18T00:30:55Z"},{"alias_kind":"arxiv_version","alias_value":"0908.1197v3","created_at":"2026-05-18T00:30:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0908.1197","created_at":"2026-05-18T00:30:55Z"},{"alias_kind":"pith_short_12","alias_value":"EZJ3LBEJ5A3E","created_at":"2026-05-18T12:25:59Z"},{"alias_kind":"pith_short_16","alias_value":"EZJ3LBEJ5A3E66NE","created_at":"2026-05-18T12:25:59Z"},{"alias_kind":"pith_short_8","alias_value":"EZJ3LBEJ","created_at":"2026-05-18T12:25:59Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2009:EZJ3LBEJ5A3E66NE2VTGEOB4KS","target":"record","payload":{"canonical_record":{"source":{"id":"0908.1197","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2009-08-08T22:13:51Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"1a0f75404733455931ba351558c909b151cc2f7ca1aef60a578dc58a17a06659","abstract_canon_sha256":"921f7d55f73b33c3aa039b2a774af8bb8b2a38890a42dd571a3f5495f25b9434"},"schema_version":"1.0"},"canonical_sha256":"2653b58489e8364f79a4d56662383c54998213961833972bc3bd344802518194","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:30:55.771465Z","signature_b64":"Xf56DlQzeJIY8sq17/lK/pLsOnybvzWfBIYe4aC5bM8EZwioKQgBgjHSh4tC5rQtUjhD8clUISppz15Ry1WoDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2653b58489e8364f79a4d56662383c54998213961833972bc3bd344802518194","last_reissued_at":"2026-05-18T00:30:55.770867Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:30:55.770867Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0908.1197","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":"2026-05-18T00:30:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QUbB2W8CtMaDEtFJPqHcM+kBGUUMdc0Av1enfiX7GXpxilYx5BvfWGRaqthnU6coaXE4i1cTrAueFwkNEjgEDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T05:18:51.576362Z"},"content_sha256":"78af611de209281728f47d3aefb6f1a2fbbc48994d6d8f653fef9c66d337a64a","schema_version":"1.0","event_id":"sha256:78af611de209281728f47d3aefb6f1a2fbbc48994d6d8f653fef9c66d337a64a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2009:EZJ3LBEJ5A3E66NE2VTGEOB4KS","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A Riemann-Roch theorem for edge-weighted graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.AG","authors_text":"Rick Miranda, Rodney James","submitted_at":"2009-08-08T22:13:51Z","abstract_excerpt":"We prove a Riemann-Roch theorem for real divisors on edge-weighted graphs over the reals, extending the result of Baker and Norine for integral divisors on graphs with multiple edges."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0908.1197","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":"2026-05-18T00:30:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"buYvaAPFB6x45vWG/+CyeXhrJZ85bfd78tzgineN3W2FAwQiUMFM7n+z7dD8N+TdaAtWseF7KYYUmdOBKMW/AA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T05:18:51.576737Z"},"content_sha256":"afede3bcd23d55d3c1f811fc480079879fa69badaa5ce430043f9415775299c0","schema_version":"1.0","event_id":"sha256:afede3bcd23d55d3c1f811fc480079879fa69badaa5ce430043f9415775299c0"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/EZJ3LBEJ5A3E66NE2VTGEOB4KS/bundle.json","state_url":"https://pith.science/pith/EZJ3LBEJ5A3E66NE2VTGEOB4KS/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/EZJ3LBEJ5A3E66NE2VTGEOB4KS/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":"2026-05-27T05:18:51Z","links":{"resolver":"https://pith.science/pith/EZJ3LBEJ5A3E66NE2VTGEOB4KS","bundle":"https://pith.science/pith/EZJ3LBEJ5A3E66NE2VTGEOB4KS/bundle.json","state":"https://pith.science/pith/EZJ3LBEJ5A3E66NE2VTGEOB4KS/state.json","well_known_bundle":"https://pith.science/.well-known/pith/EZJ3LBEJ5A3E66NE2VTGEOB4KS/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:EZJ3LBEJ5A3E66NE2VTGEOB4KS","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":"921f7d55f73b33c3aa039b2a774af8bb8b2a38890a42dd571a3f5495f25b9434","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2009-08-08T22:13:51Z","title_canon_sha256":"1a0f75404733455931ba351558c909b151cc2f7ca1aef60a578dc58a17a06659"},"schema_version":"1.0","source":{"id":"0908.1197","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0908.1197","created_at":"2026-05-18T00:30:55Z"},{"alias_kind":"arxiv_version","alias_value":"0908.1197v3","created_at":"2026-05-18T00:30:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0908.1197","created_at":"2026-05-18T00:30:55Z"},{"alias_kind":"pith_short_12","alias_value":"EZJ3LBEJ5A3E","created_at":"2026-05-18T12:25:59Z"},{"alias_kind":"pith_short_16","alias_value":"EZJ3LBEJ5A3E66NE","created_at":"2026-05-18T12:25:59Z"},{"alias_kind":"pith_short_8","alias_value":"EZJ3LBEJ","created_at":"2026-05-18T12:25:59Z"}],"graph_snapshots":[{"event_id":"sha256:afede3bcd23d55d3c1f811fc480079879fa69badaa5ce430043f9415775299c0","target":"graph","created_at":"2026-05-18T00:30:55Z","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":"We prove a Riemann-Roch theorem for real divisors on edge-weighted graphs over the reals, extending the result of Baker and Norine for integral divisors on graphs with multiple edges.","authors_text":"Rick Miranda, Rodney James","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2009-08-08T22:13:51Z","title":"A Riemann-Roch theorem for edge-weighted graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0908.1197","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":"sha256:78af611de209281728f47d3aefb6f1a2fbbc48994d6d8f653fef9c66d337a64a","target":"record","created_at":"2026-05-18T00:30:55Z","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":"921f7d55f73b33c3aa039b2a774af8bb8b2a38890a42dd571a3f5495f25b9434","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2009-08-08T22:13:51Z","title_canon_sha256":"1a0f75404733455931ba351558c909b151cc2f7ca1aef60a578dc58a17a06659"},"schema_version":"1.0","source":{"id":"0908.1197","kind":"arxiv","version":3}},"canonical_sha256":"2653b58489e8364f79a4d56662383c54998213961833972bc3bd344802518194","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2653b58489e8364f79a4d56662383c54998213961833972bc3bd344802518194","first_computed_at":"2026-05-18T00:30:55.770867Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:30:55.770867Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Xf56DlQzeJIY8sq17/lK/pLsOnybvzWfBIYe4aC5bM8EZwioKQgBgjHSh4tC5rQtUjhD8clUISppz15Ry1WoDw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:30:55.771465Z","signed_message":"canonical_sha256_bytes"},"source_id":"0908.1197","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:78af611de209281728f47d3aefb6f1a2fbbc48994d6d8f653fef9c66d337a64a","sha256:afede3bcd23d55d3c1f811fc480079879fa69badaa5ce430043f9415775299c0"],"state_sha256":"c05da3c28a04824994757bd979c9562afe4fc0e246da46d54becff9012a97e2c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YggyAym0KKE8wNliMFgW33KULFYEbBVmV81yc40ql1cTbA9YB3tJxdnbtviJSdRebSWM0aYfAlTVkfzxbmNwCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T05:18:51.579041Z","bundle_sha256":"10478e16e08653e861ac97832ae3d1b9875b453d060ae2f0ec45eb3b8b3cd34d"}}