{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:LKYQ4MPGBH6GBA4CSVI3ZRBJOU","short_pith_number":"pith:LKYQ4MPG","canonical_record":{"source":{"id":"1506.01168","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-06-03T09:02:22Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"f7b6f0e1125d9a00a66a041185a4c0b93f1f4cd418f0d0272ca22f7c50e220b9","abstract_canon_sha256":"cfa1b51b3203948e4475c732281f4b2df9fdf291237d94877e0545718bd02914"},"schema_version":"1.0"},"canonical_sha256":"5ab10e31e609fc6083829551bcc429753340726e2a6c2e0d1b4497e5048748ff","source":{"kind":"arxiv","id":"1506.01168","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1506.01168","created_at":"2026-05-18T01:05:46Z"},{"alias_kind":"arxiv_version","alias_value":"1506.01168v1","created_at":"2026-05-18T01:05:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1506.01168","created_at":"2026-05-18T01:05:46Z"},{"alias_kind":"pith_short_12","alias_value":"LKYQ4MPGBH6G","created_at":"2026-05-18T12:29:29Z"},{"alias_kind":"pith_short_16","alias_value":"LKYQ4MPGBH6GBA4C","created_at":"2026-05-18T12:29:29Z"},{"alias_kind":"pith_short_8","alias_value":"LKYQ4MPG","created_at":"2026-05-18T12:29:29Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:LKYQ4MPGBH6GBA4CSVI3ZRBJOU","target":"record","payload":{"canonical_record":{"source":{"id":"1506.01168","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-06-03T09:02:22Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"f7b6f0e1125d9a00a66a041185a4c0b93f1f4cd418f0d0272ca22f7c50e220b9","abstract_canon_sha256":"cfa1b51b3203948e4475c732281f4b2df9fdf291237d94877e0545718bd02914"},"schema_version":"1.0"},"canonical_sha256":"5ab10e31e609fc6083829551bcc429753340726e2a6c2e0d1b4497e5048748ff","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:05:46.293737Z","signature_b64":"a7Y6tiVT10s1ket/XeWgnfg8xMkJrIkmtqCYJIwK285BMhvbrLqxleotO/igl3d/G7kA4C4XUmSkmJaN7r+tAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5ab10e31e609fc6083829551bcc429753340726e2a6c2e0d1b4497e5048748ff","last_reissued_at":"2026-05-18T01:05:46.293230Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:05:46.293230Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1506.01168","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":"2026-05-18T01:05:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tsWktI9uwsSVBb2w8zZ8v2PL32jv0Mmv7LJRX6698McaYx3+Nx7+sOKBKVwhl8RZgyxNQxe42UlhDnKZFWheCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T12:39:33.859699Z"},"content_sha256":"ceb0041a62a408e68071be86ac528f989f5337a1d008c9cfd3c6010cfab593ef","schema_version":"1.0","event_id":"sha256:ceb0041a62a408e68071be86ac528f989f5337a1d008c9cfd3c6010cfab593ef"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:LKYQ4MPGBH6GBA4CSVI3ZRBJOU","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Numerical Adjunction Formulas for Weighted Projective Planes and Lattice Points Counting","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.AG","authors_text":"J.I. Cogolludo-Agustin, J. Martin-Morales, J. Ortigas-Galindo","submitted_at":"2015-06-03T09:02:22Z","abstract_excerpt":"This paper gives an explicit formula for the Ehrhart quasi-polynomial of certain 2-dimensional polyhedra in terms of invariants of surface quotient singularities. Also, a formula for the dimension of the space of quasi-homogeneous polynomials of a given degree is derived. This admits an interpretation as a Numerical Adjunction Formula for singular curves on the weighted projective plane."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.01168","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":"2026-05-18T01:05:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CgOqh22JMHErdWz4D/fH+W2BH4YFoU1eLPkGTFrzZsV9M0visADNBYs/LLxhNVvfEfTTZz0PNFM8iSN2x69PAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T12:39:33.860046Z"},"content_sha256":"a6027db5453bae568fd7c5c884b254e045ed1cf899e069836fa033411fe5321a","schema_version":"1.0","event_id":"sha256:a6027db5453bae568fd7c5c884b254e045ed1cf899e069836fa033411fe5321a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/LKYQ4MPGBH6GBA4CSVI3ZRBJOU/bundle.json","state_url":"https://pith.science/pith/LKYQ4MPGBH6GBA4CSVI3ZRBJOU/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/LKYQ4MPGBH6GBA4CSVI3ZRBJOU/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":"2026-06-08T12:39:33Z","links":{"resolver":"https://pith.science/pith/LKYQ4MPGBH6GBA4CSVI3ZRBJOU","bundle":"https://pith.science/pith/LKYQ4MPGBH6GBA4CSVI3ZRBJOU/bundle.json","state":"https://pith.science/pith/LKYQ4MPGBH6GBA4CSVI3ZRBJOU/state.json","well_known_bundle":"https://pith.science/.well-known/pith/LKYQ4MPGBH6GBA4CSVI3ZRBJOU/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:LKYQ4MPGBH6GBA4CSVI3ZRBJOU","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":"cfa1b51b3203948e4475c732281f4b2df9fdf291237d94877e0545718bd02914","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-06-03T09:02:22Z","title_canon_sha256":"f7b6f0e1125d9a00a66a041185a4c0b93f1f4cd418f0d0272ca22f7c50e220b9"},"schema_version":"1.0","source":{"id":"1506.01168","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1506.01168","created_at":"2026-05-18T01:05:46Z"},{"alias_kind":"arxiv_version","alias_value":"1506.01168v1","created_at":"2026-05-18T01:05:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1506.01168","created_at":"2026-05-18T01:05:46Z"},{"alias_kind":"pith_short_12","alias_value":"LKYQ4MPGBH6G","created_at":"2026-05-18T12:29:29Z"},{"alias_kind":"pith_short_16","alias_value":"LKYQ4MPGBH6GBA4C","created_at":"2026-05-18T12:29:29Z"},{"alias_kind":"pith_short_8","alias_value":"LKYQ4MPG","created_at":"2026-05-18T12:29:29Z"}],"graph_snapshots":[{"event_id":"sha256:a6027db5453bae568fd7c5c884b254e045ed1cf899e069836fa033411fe5321a","target":"graph","created_at":"2026-05-18T01:05:46Z","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":"This paper gives an explicit formula for the Ehrhart quasi-polynomial of certain 2-dimensional polyhedra in terms of invariants of surface quotient singularities. Also, a formula for the dimension of the space of quasi-homogeneous polynomials of a given degree is derived. This admits an interpretation as a Numerical Adjunction Formula for singular curves on the weighted projective plane.","authors_text":"J.I. Cogolludo-Agustin, J. Martin-Morales, J. Ortigas-Galindo","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-06-03T09:02:22Z","title":"Numerical Adjunction Formulas for Weighted Projective Planes and Lattice Points Counting"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.01168","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:ceb0041a62a408e68071be86ac528f989f5337a1d008c9cfd3c6010cfab593ef","target":"record","created_at":"2026-05-18T01:05:46Z","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":"cfa1b51b3203948e4475c732281f4b2df9fdf291237d94877e0545718bd02914","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-06-03T09:02:22Z","title_canon_sha256":"f7b6f0e1125d9a00a66a041185a4c0b93f1f4cd418f0d0272ca22f7c50e220b9"},"schema_version":"1.0","source":{"id":"1506.01168","kind":"arxiv","version":1}},"canonical_sha256":"5ab10e31e609fc6083829551bcc429753340726e2a6c2e0d1b4497e5048748ff","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5ab10e31e609fc6083829551bcc429753340726e2a6c2e0d1b4497e5048748ff","first_computed_at":"2026-05-18T01:05:46.293230Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:05:46.293230Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"a7Y6tiVT10s1ket/XeWgnfg8xMkJrIkmtqCYJIwK285BMhvbrLqxleotO/igl3d/G7kA4C4XUmSkmJaN7r+tAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:05:46.293737Z","signed_message":"canonical_sha256_bytes"},"source_id":"1506.01168","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ceb0041a62a408e68071be86ac528f989f5337a1d008c9cfd3c6010cfab593ef","sha256:a6027db5453bae568fd7c5c884b254e045ed1cf899e069836fa033411fe5321a"],"state_sha256":"dc32118e03dc04f09b46bd892c8abd705e3245c38bdc5021fc0dce424fdb209f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dEw6r0wq95LavLhQGt7PagIEJu2DQjONZS5ALqU1b67SYQpmTJZB9M1yOAahct/YV2Tb457R7XTAhHRZ+EftBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-08T12:39:33.862120Z","bundle_sha256":"a7c2696c9db5870ab9ccf4d6b8e103b6376d21c939db1590afd8dac76196ddf0"}}