{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:USO4PYLT3LSCNDPCYP4HQNVDQS","short_pith_number":"pith:USO4PYLT","canonical_record":{"source":{"id":"1403.4048","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-03-17T09:55:30Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"c0df4b9dc879d7279f8d29313012a9645cce4fc7bac10d50bd2e9c70dfb59f5f","abstract_canon_sha256":"7be11bf80757462da795081b945657bdd0ced9e57d6ab58f1a5e8776339f333d"},"schema_version":"1.0"},"canonical_sha256":"a49dc7e173dae4268de2c3f87836a38481cf069cabe4a97034ad56c7aef7f2ad","source":{"kind":"arxiv","id":"1403.4048","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1403.4048","created_at":"2026-05-18T01:33:57Z"},{"alias_kind":"arxiv_version","alias_value":"1403.4048v2","created_at":"2026-05-18T01:33:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1403.4048","created_at":"2026-05-18T01:33:57Z"},{"alias_kind":"pith_short_12","alias_value":"USO4PYLT3LSC","created_at":"2026-05-18T12:28:52Z"},{"alias_kind":"pith_short_16","alias_value":"USO4PYLT3LSCNDPC","created_at":"2026-05-18T12:28:52Z"},{"alias_kind":"pith_short_8","alias_value":"USO4PYLT","created_at":"2026-05-18T12:28:52Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:USO4PYLT3LSCNDPCYP4HQNVDQS","target":"record","payload":{"canonical_record":{"source":{"id":"1403.4048","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-03-17T09:55:30Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"c0df4b9dc879d7279f8d29313012a9645cce4fc7bac10d50bd2e9c70dfb59f5f","abstract_canon_sha256":"7be11bf80757462da795081b945657bdd0ced9e57d6ab58f1a5e8776339f333d"},"schema_version":"1.0"},"canonical_sha256":"a49dc7e173dae4268de2c3f87836a38481cf069cabe4a97034ad56c7aef7f2ad","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:33:57.108327Z","signature_b64":"sEDIb+elPMJ15zyzp1bn2gmGI73ypScSgj1o6ZG25fgHxA9c+Yr0k+bWPdm6HoU4cxs9LtlLan1YHwGhxy1QDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a49dc7e173dae4268de2c3f87836a38481cf069cabe4a97034ad56c7aef7f2ad","last_reissued_at":"2026-05-18T01:33:57.107970Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:33:57.107970Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1403.4048","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":"2026-05-18T01:33:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tBUxvq5sacSL4k+Jf+1au2+ogTxiRPD6GKczkiZCu8BhPPupmYvPvys59QUCnpw5N3qgQUD+NvBgLmTHISMODA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T21:53:47.306921Z"},"content_sha256":"468e59e929eef804bac58d0d0aa2ee08106e53a185d669a914f943853c307382","schema_version":"1.0","event_id":"sha256:468e59e929eef804bac58d0d0aa2ee08106e53a185d669a914f943853c307382"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:USO4PYLT3LSCNDPCYP4HQNVDQS","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Successive minima of toric height functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.NT","authors_text":"Jose Ignacio Burgos Gil, Martin Sombra, Patrice Philippon","submitted_at":"2014-03-17T09:55:30Z","abstract_excerpt":"Given a toric metrized R-divisor on a toric variety over a global field, we give a formula for the essential minimum of the associated height function. Under suitable positivity conditions, we also give formulae for all the successive minima. We apply these results to the study, in the toric setting, of the relation between the successive minima and other arithmetic invariants like the height and the arithmetic volume. We also apply our formulae to compute the successive minima for several families of examples, including weighted projective spaces, toric bundles and translates of subtori."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.4048","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":"2026-05-18T01:33:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"iMs5A0MgkSsgUgIAiczw7l56KEuV77m2UQWO2ieZeu5yOsWg6OAFHndVpH5n8KA0xjkJYPPAZ7OJviVSL31iBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T21:53:47.307254Z"},"content_sha256":"7682d88796edb2002abddf7a624e0301226da1f210b004ea4df9d8e213d1778c","schema_version":"1.0","event_id":"sha256:7682d88796edb2002abddf7a624e0301226da1f210b004ea4df9d8e213d1778c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/USO4PYLT3LSCNDPCYP4HQNVDQS/bundle.json","state_url":"https://pith.science/pith/USO4PYLT3LSCNDPCYP4HQNVDQS/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/USO4PYLT3LSCNDPCYP4HQNVDQS/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":"2026-06-22T21:53:47Z","links":{"resolver":"https://pith.science/pith/USO4PYLT3LSCNDPCYP4HQNVDQS","bundle":"https://pith.science/pith/USO4PYLT3LSCNDPCYP4HQNVDQS/bundle.json","state":"https://pith.science/pith/USO4PYLT3LSCNDPCYP4HQNVDQS/state.json","well_known_bundle":"https://pith.science/.well-known/pith/USO4PYLT3LSCNDPCYP4HQNVDQS/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:USO4PYLT3LSCNDPCYP4HQNVDQS","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":"7be11bf80757462da795081b945657bdd0ced9e57d6ab58f1a5e8776339f333d","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-03-17T09:55:30Z","title_canon_sha256":"c0df4b9dc879d7279f8d29313012a9645cce4fc7bac10d50bd2e9c70dfb59f5f"},"schema_version":"1.0","source":{"id":"1403.4048","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1403.4048","created_at":"2026-05-18T01:33:57Z"},{"alias_kind":"arxiv_version","alias_value":"1403.4048v2","created_at":"2026-05-18T01:33:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1403.4048","created_at":"2026-05-18T01:33:57Z"},{"alias_kind":"pith_short_12","alias_value":"USO4PYLT3LSC","created_at":"2026-05-18T12:28:52Z"},{"alias_kind":"pith_short_16","alias_value":"USO4PYLT3LSCNDPC","created_at":"2026-05-18T12:28:52Z"},{"alias_kind":"pith_short_8","alias_value":"USO4PYLT","created_at":"2026-05-18T12:28:52Z"}],"graph_snapshots":[{"event_id":"sha256:7682d88796edb2002abddf7a624e0301226da1f210b004ea4df9d8e213d1778c","target":"graph","created_at":"2026-05-18T01:33:57Z","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":"Given a toric metrized R-divisor on a toric variety over a global field, we give a formula for the essential minimum of the associated height function. Under suitable positivity conditions, we also give formulae for all the successive minima. We apply these results to the study, in the toric setting, of the relation between the successive minima and other arithmetic invariants like the height and the arithmetic volume. We also apply our formulae to compute the successive minima for several families of examples, including weighted projective spaces, toric bundles and translates of subtori.","authors_text":"Jose Ignacio Burgos Gil, Martin Sombra, Patrice Philippon","cross_cats":["math.AG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-03-17T09:55:30Z","title":"Successive minima of toric height functions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.4048","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":"sha256:468e59e929eef804bac58d0d0aa2ee08106e53a185d669a914f943853c307382","target":"record","created_at":"2026-05-18T01:33:57Z","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":"7be11bf80757462da795081b945657bdd0ced9e57d6ab58f1a5e8776339f333d","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-03-17T09:55:30Z","title_canon_sha256":"c0df4b9dc879d7279f8d29313012a9645cce4fc7bac10d50bd2e9c70dfb59f5f"},"schema_version":"1.0","source":{"id":"1403.4048","kind":"arxiv","version":2}},"canonical_sha256":"a49dc7e173dae4268de2c3f87836a38481cf069cabe4a97034ad56c7aef7f2ad","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a49dc7e173dae4268de2c3f87836a38481cf069cabe4a97034ad56c7aef7f2ad","first_computed_at":"2026-05-18T01:33:57.107970Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:33:57.107970Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"sEDIb+elPMJ15zyzp1bn2gmGI73ypScSgj1o6ZG25fgHxA9c+Yr0k+bWPdm6HoU4cxs9LtlLan1YHwGhxy1QDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:33:57.108327Z","signed_message":"canonical_sha256_bytes"},"source_id":"1403.4048","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:468e59e929eef804bac58d0d0aa2ee08106e53a185d669a914f943853c307382","sha256:7682d88796edb2002abddf7a624e0301226da1f210b004ea4df9d8e213d1778c"],"state_sha256":"ca6da381c4f6a4f209a705c655fff7d1ca46314bfc4c363d049a2f2b48d7965e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mSQ9Wb/yHqyQSMhx1sl8372GJHdedVIo4FSCZtEreYZFFMxEicOIrqR/O3an+iclo2UUW6L0qMOatGUkc5EJAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-22T21:53:47.309071Z","bundle_sha256":"7eebfd2983a53a85edc50f78807f2873dc8f5e7b807e11f62619ad0b105d697a"}}