{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:X4YIGQ5UJTRVOFSUD6BOPHPXMY","short_pith_number":"pith:X4YIGQ5U","canonical_record":{"source":{"id":"1001.5081","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2010-01-28T02:14:36Z","cross_cats_sorted":[],"title_canon_sha256":"54299cdee83e6557c214d3be359ee37bda1a80e5a002593b5b98e196e22ee1d3","abstract_canon_sha256":"228347b1a808dd47376f78b57a2d86742b4556114e4d5f3a775e305a9eaee422"},"schema_version":"1.0"},"canonical_sha256":"bf308343b44ce35716541f82e79df76612fa22be9910f0389259f2b8e3dab1ff","source":{"kind":"arxiv","id":"1001.5081","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1001.5081","created_at":"2026-05-18T04:08:24Z"},{"alias_kind":"arxiv_version","alias_value":"1001.5081v2","created_at":"2026-05-18T04:08:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1001.5081","created_at":"2026-05-18T04:08:24Z"},{"alias_kind":"pith_short_12","alias_value":"X4YIGQ5UJTRV","created_at":"2026-05-18T12:26:17Z"},{"alias_kind":"pith_short_16","alias_value":"X4YIGQ5UJTRVOFSU","created_at":"2026-05-18T12:26:17Z"},{"alias_kind":"pith_short_8","alias_value":"X4YIGQ5U","created_at":"2026-05-18T12:26:17Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:X4YIGQ5UJTRVOFSUD6BOPHPXMY","target":"record","payload":{"canonical_record":{"source":{"id":"1001.5081","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2010-01-28T02:14:36Z","cross_cats_sorted":[],"title_canon_sha256":"54299cdee83e6557c214d3be359ee37bda1a80e5a002593b5b98e196e22ee1d3","abstract_canon_sha256":"228347b1a808dd47376f78b57a2d86742b4556114e4d5f3a775e305a9eaee422"},"schema_version":"1.0"},"canonical_sha256":"bf308343b44ce35716541f82e79df76612fa22be9910f0389259f2b8e3dab1ff","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:08:24.697409Z","signature_b64":"A5qmMZvD4SO0dfTKKyJG1X7rD9Yuutm2EvQvZaQZvLCC9VoSMkerVfu5qnVHZXS/kDZ+zvoWC/ZBGaf4OZdWBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bf308343b44ce35716541f82e79df76612fa22be9910f0389259f2b8e3dab1ff","last_reissued_at":"2026-05-18T04:08:24.696806Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:08:24.696806Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1001.5081","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:08:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"oqKIOWiBij1CwC8kqbqNEkyzpo+LW75WRFHT4xHDy7P54TC4DswVjSPza+I3rVwwUJdI2asarimpqj8t92vvBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T05:22:41.806077Z"},"content_sha256":"4e1014082064db9e128f1aa43ee7dced7a1903002e5e06a0ab251528e2effbc6","schema_version":"1.0","event_id":"sha256:4e1014082064db9e128f1aa43ee7dced7a1903002e5e06a0ab251528e2effbc6"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:X4YIGQ5UJTRVOFSUD6BOPHPXMY","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Siegel's mass formula and averages of Dirichlet L-functions over function fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Jorge Morales, Piotr Maciak","submitted_at":"2010-01-28T02:14:36Z","abstract_excerpt":"Let D be a square-free polynomial in F_q[t], where q is odd, and let G be a genus of definite ternary lattices over F_q[t] of determinant D. In this paper we give self-contained and relatively elementary proofs of Siegel's formulas for the weighted sum of primitive representations numbers over the classes of G and for the mass of G. Our proof of the mass formula shows an interesting relation with certain averages of Dirichlet L-functions."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1001.5081","kind":"arxiv","version":2},"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":"2026-05-18T04:08:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sb2KfC5h4u0Hz8JghZ0FX+3BgRwQk67V8i6DPd7+HjGvpBE1QnWbAVGFfAbgb2XzkvbA7K6MuhcIFjEBrusXCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T05:22:41.806426Z"},"content_sha256":"bf12dab277aa062368a8dfbcab2895a8cd173bcf54f5d5dc1a583a2e81d8effb","schema_version":"1.0","event_id":"sha256:bf12dab277aa062368a8dfbcab2895a8cd173bcf54f5d5dc1a583a2e81d8effb"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/X4YIGQ5UJTRVOFSUD6BOPHPXMY/bundle.json","state_url":"https://pith.science/pith/X4YIGQ5UJTRVOFSUD6BOPHPXMY/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/X4YIGQ5UJTRVOFSUD6BOPHPXMY/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":"2026-06-01T05:22:41Z","links":{"resolver":"https://pith.science/pith/X4YIGQ5UJTRVOFSUD6BOPHPXMY","bundle":"https://pith.science/pith/X4YIGQ5UJTRVOFSUD6BOPHPXMY/bundle.json","state":"https://pith.science/pith/X4YIGQ5UJTRVOFSUD6BOPHPXMY/state.json","well_known_bundle":"https://pith.science/.well-known/pith/X4YIGQ5UJTRVOFSUD6BOPHPXMY/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:X4YIGQ5UJTRVOFSUD6BOPHPXMY","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":"228347b1a808dd47376f78b57a2d86742b4556114e4d5f3a775e305a9eaee422","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2010-01-28T02:14:36Z","title_canon_sha256":"54299cdee83e6557c214d3be359ee37bda1a80e5a002593b5b98e196e22ee1d3"},"schema_version":"1.0","source":{"id":"1001.5081","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1001.5081","created_at":"2026-05-18T04:08:24Z"},{"alias_kind":"arxiv_version","alias_value":"1001.5081v2","created_at":"2026-05-18T04:08:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1001.5081","created_at":"2026-05-18T04:08:24Z"},{"alias_kind":"pith_short_12","alias_value":"X4YIGQ5UJTRV","created_at":"2026-05-18T12:26:17Z"},{"alias_kind":"pith_short_16","alias_value":"X4YIGQ5UJTRVOFSU","created_at":"2026-05-18T12:26:17Z"},{"alias_kind":"pith_short_8","alias_value":"X4YIGQ5U","created_at":"2026-05-18T12:26:17Z"}],"graph_snapshots":[{"event_id":"sha256:bf12dab277aa062368a8dfbcab2895a8cd173bcf54f5d5dc1a583a2e81d8effb","target":"graph","created_at":"2026-05-18T04:08:24Z","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":"Let D be a square-free polynomial in F_q[t], where q is odd, and let G be a genus of definite ternary lattices over F_q[t] of determinant D. In this paper we give self-contained and relatively elementary proofs of Siegel's formulas for the weighted sum of primitive representations numbers over the classes of G and for the mass of G. Our proof of the mass formula shows an interesting relation with certain averages of Dirichlet L-functions.","authors_text":"Jorge Morales, Piotr Maciak","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2010-01-28T02:14:36Z","title":"Siegel's mass formula and averages of Dirichlet L-functions over function fields"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1001.5081","kind":"arxiv","version":2},"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":"sha256:4e1014082064db9e128f1aa43ee7dced7a1903002e5e06a0ab251528e2effbc6","target":"record","created_at":"2026-05-18T04:08:24Z","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":"228347b1a808dd47376f78b57a2d86742b4556114e4d5f3a775e305a9eaee422","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2010-01-28T02:14:36Z","title_canon_sha256":"54299cdee83e6557c214d3be359ee37bda1a80e5a002593b5b98e196e22ee1d3"},"schema_version":"1.0","source":{"id":"1001.5081","kind":"arxiv","version":2}},"canonical_sha256":"bf308343b44ce35716541f82e79df76612fa22be9910f0389259f2b8e3dab1ff","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bf308343b44ce35716541f82e79df76612fa22be9910f0389259f2b8e3dab1ff","first_computed_at":"2026-05-18T04:08:24.696806Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:08:24.696806Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"A5qmMZvD4SO0dfTKKyJG1X7rD9Yuutm2EvQvZaQZvLCC9VoSMkerVfu5qnVHZXS/kDZ+zvoWC/ZBGaf4OZdWBA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:08:24.697409Z","signed_message":"canonical_sha256_bytes"},"source_id":"1001.5081","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4e1014082064db9e128f1aa43ee7dced7a1903002e5e06a0ab251528e2effbc6","sha256:bf12dab277aa062368a8dfbcab2895a8cd173bcf54f5d5dc1a583a2e81d8effb"],"state_sha256":"b5f3cf1e2df60c58b5175519f9d8096c81983e45fb7dea2e2b8fd51b7ada5437"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2+c7aT/uHpQVUN93ClYDqZzM/dZWkXQMY2fbSj4XgAoKZ/EhhDLORC29oZUxZY8fydamymUNYYbNj9YVQsGFAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T05:22:41.808338Z","bundle_sha256":"8b9b4d3c146c52fbd8d79da5fef2634120af95c43cd3899509f13f332867a1be"}}