{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:PZFECHFHSTLXD5A34PR7BS7XGL","short_pith_number":"pith:PZFECHFH","canonical_record":{"source":{"id":"2408.07631","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2024-08-14T15:57:28Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"bdee3c3b4f78005128ce4e8d8ae5804690af6fd6d59cc348a37964c9799c298c","abstract_canon_sha256":"1878b46d7d615d8bd8b0070924eb6fbaba05275a8e874676741f3842ae6f8f14"},"schema_version":"1.0"},"canonical_sha256":"7e4a411ca794d771f41be3e3f0cbf732d0f90af2a71bd19d550bc9ab491d8df6","source":{"kind":"arxiv","id":"2408.07631","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2408.07631","created_at":"2026-07-05T09:10:32Z"},{"alias_kind":"arxiv_version","alias_value":"2408.07631v2","created_at":"2026-07-05T09:10:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2408.07631","created_at":"2026-07-05T09:10:32Z"},{"alias_kind":"pith_short_12","alias_value":"PZFECHFHSTLX","created_at":"2026-07-05T09:10:32Z"},{"alias_kind":"pith_short_16","alias_value":"PZFECHFHSTLXD5A3","created_at":"2026-07-05T09:10:32Z"},{"alias_kind":"pith_short_8","alias_value":"PZFECHFH","created_at":"2026-07-05T09:10:32Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:PZFECHFHSTLXD5A34PR7BS7XGL","target":"record","payload":{"canonical_record":{"source":{"id":"2408.07631","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2024-08-14T15:57:28Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"bdee3c3b4f78005128ce4e8d8ae5804690af6fd6d59cc348a37964c9799c298c","abstract_canon_sha256":"1878b46d7d615d8bd8b0070924eb6fbaba05275a8e874676741f3842ae6f8f14"},"schema_version":"1.0"},"canonical_sha256":"7e4a411ca794d771f41be3e3f0cbf732d0f90af2a71bd19d550bc9ab491d8df6","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:10:32.376350Z","signature_b64":"PEUxprxgrSqlrUs+YzSHSLq13M0023higbOggRLSTHEW9dUbf5Xnn1q0Xhc/OjDYBxRsWcn1qGnySIUnH9ydCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7e4a411ca794d771f41be3e3f0cbf732d0f90af2a71bd19d550bc9ab491d8df6","last_reissued_at":"2026-07-05T09:10:32.375864Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:10:32.375864Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2408.07631","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":"2026-07-05T09:10:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yTgTW8Sw0ExkPcrII7dy/L5YvK8j0IVQ05HYs0hVV9Wwizm4Wchqs49lZqUSZMy3TAnNMUgigxhZ8slcgdlYBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-05T04:52:56.567409Z"},"content_sha256":"3433fb27b845f1bb84badfe6c7b30cebaf520ff54ab0d905cd53cf499c554a51","schema_version":"1.0","event_id":"sha256:3433fb27b845f1bb84badfe6c7b30cebaf520ff54ab0d905cd53cf499c554a51"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:PZFECHFHSTLXD5A34PR7BS7XGL","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Counting rational points on Hirzebruch-Kleinschmidt varieties over global function fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.NT","authors_text":"Pedro Montero, Sebasti\\'an Herrero, Tob\\'ias Mart\\'inez","submitted_at":"2024-08-14T15:57:28Z","abstract_excerpt":"Inspired by Bourqui's work on anticanonical height zeta functions on Hirzebruch surfaces, we study height zeta functions of split toric varieties with Picard rank 2 over global function fields, with respect to height functions associated with big metrized line bundles. We show that these varieties can be naturally decomposed into a finite disjoint union of subvarieties, where precise analytic properties of the corresponding height zeta functions can be given. As application, we obtain asymptotic formulas for the number of rational points of large height on each subvariety, with explicit leadin"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2408.07631","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2408.07631/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T09:10:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WGai3cGArvaCaWfBR81wr1AyivG/SoiFwIsfuerr8rdt68lvuW1QGVJDNL0v1jLJhVn6hMdN9FtDUjmmB+f8BA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-05T04:52:56.568348Z"},"content_sha256":"57fac0e44f1ac6691ee2f654fcaab6f4d23fb6583a49b219650930af83716dda","schema_version":"1.0","event_id":"sha256:57fac0e44f1ac6691ee2f654fcaab6f4d23fb6583a49b219650930af83716dda"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/PZFECHFHSTLXD5A34PR7BS7XGL/bundle.json","state_url":"https://pith.science/pith/PZFECHFHSTLXD5A34PR7BS7XGL/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/PZFECHFHSTLXD5A34PR7BS7XGL/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":"2026-08-05T04:52:56Z","links":{"resolver":"https://pith.science/pith/PZFECHFHSTLXD5A34PR7BS7XGL","bundle":"https://pith.science/pith/PZFECHFHSTLXD5A34PR7BS7XGL/bundle.json","state":"https://pith.science/pith/PZFECHFHSTLXD5A34PR7BS7XGL/state.json","well_known_bundle":"https://pith.science/.well-known/pith/PZFECHFHSTLXD5A34PR7BS7XGL/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:PZFECHFHSTLXD5A34PR7BS7XGL","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":"1878b46d7d615d8bd8b0070924eb6fbaba05275a8e874676741f3842ae6f8f14","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2024-08-14T15:57:28Z","title_canon_sha256":"bdee3c3b4f78005128ce4e8d8ae5804690af6fd6d59cc348a37964c9799c298c"},"schema_version":"1.0","source":{"id":"2408.07631","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2408.07631","created_at":"2026-07-05T09:10:32Z"},{"alias_kind":"arxiv_version","alias_value":"2408.07631v2","created_at":"2026-07-05T09:10:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2408.07631","created_at":"2026-07-05T09:10:32Z"},{"alias_kind":"pith_short_12","alias_value":"PZFECHFHSTLX","created_at":"2026-07-05T09:10:32Z"},{"alias_kind":"pith_short_16","alias_value":"PZFECHFHSTLXD5A3","created_at":"2026-07-05T09:10:32Z"},{"alias_kind":"pith_short_8","alias_value":"PZFECHFH","created_at":"2026-07-05T09:10:32Z"}],"graph_snapshots":[{"event_id":"sha256:57fac0e44f1ac6691ee2f654fcaab6f4d23fb6583a49b219650930af83716dda","target":"graph","created_at":"2026-07-05T09:10:32Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2408.07631/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Inspired by Bourqui's work on anticanonical height zeta functions on Hirzebruch surfaces, we study height zeta functions of split toric varieties with Picard rank 2 over global function fields, with respect to height functions associated with big metrized line bundles. We show that these varieties can be naturally decomposed into a finite disjoint union of subvarieties, where precise analytic properties of the corresponding height zeta functions can be given. As application, we obtain asymptotic formulas for the number of rational points of large height on each subvariety, with explicit leadin","authors_text":"Pedro Montero, Sebasti\\'an Herrero, Tob\\'ias Mart\\'inez","cross_cats":["math.AG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2024-08-14T15:57:28Z","title":"Counting rational points on Hirzebruch-Kleinschmidt varieties over global function fields"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2408.07631","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":"sha256:3433fb27b845f1bb84badfe6c7b30cebaf520ff54ab0d905cd53cf499c554a51","target":"record","created_at":"2026-07-05T09:10:32Z","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":"1878b46d7d615d8bd8b0070924eb6fbaba05275a8e874676741f3842ae6f8f14","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2024-08-14T15:57:28Z","title_canon_sha256":"bdee3c3b4f78005128ce4e8d8ae5804690af6fd6d59cc348a37964c9799c298c"},"schema_version":"1.0","source":{"id":"2408.07631","kind":"arxiv","version":2}},"canonical_sha256":"7e4a411ca794d771f41be3e3f0cbf732d0f90af2a71bd19d550bc9ab491d8df6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7e4a411ca794d771f41be3e3f0cbf732d0f90af2a71bd19d550bc9ab491d8df6","first_computed_at":"2026-07-05T09:10:32.375864Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:10:32.375864Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"PEUxprxgrSqlrUs+YzSHSLq13M0023higbOggRLSTHEW9dUbf5Xnn1q0Xhc/OjDYBxRsWcn1qGnySIUnH9ydCg==","signature_status":"signed_v1","signed_at":"2026-07-05T09:10:32.376350Z","signed_message":"canonical_sha256_bytes"},"source_id":"2408.07631","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3433fb27b845f1bb84badfe6c7b30cebaf520ff54ab0d905cd53cf499c554a51","sha256:57fac0e44f1ac6691ee2f654fcaab6f4d23fb6583a49b219650930af83716dda"],"state_sha256":"2978da63dafd62f644e2c65ec678883c72180f71f40836311f31807cbc54ea77"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tuvrjWsB4/4rYNahGs/w8BmJGuIoPROpIQR8tBu+FMM4eg0PuiU5I2QHC2MEPTQj10+PtQjkNXR1eRY/sOQ9DA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-05T04:52:56.574025Z","bundle_sha256":"5cd4df2b3620650c258749557ca17bcf6a52f1ce4b234f671b923e4c746117e7"}}