{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:XNYLND4JRSP6ERYAGGIC6Z6WTG","short_pith_number":"pith:XNYLND4J","schema_version":"1.0","canonical_sha256":"bb70b68f898c9fe2470031902f67d699bac9a9127bd4cd42a2abb63532670e1c","source":{"kind":"arxiv","id":"1505.04740","version":2},"attestation_state":"computed","paper":{"title":"On Faltings' Delta-Invariant of Hyperelliptic Riemann Surfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.NT","authors_text":"Robert Wilms","submitted_at":"2015-05-18T18:00:21Z","abstract_excerpt":"In this paper we prove new explicit formulas for Faltings' $\\delta$-invariant of an arbitrary hyperelliptic Riemann surface. This has several applications: For example we obtain an explicit lower bound for $\\delta$ depending only on the genus, and we deduce new explicit bounds for the Arakelov self-intersection number $\\omega^2$ associated to hyperelliptic curves over number fields. Furthermore, we obtain an improved version of Szpiro's small points conjecture for hyperelliptic curves of genus at least $3$. Our method allows us in addition to establish a generalization of Rosenhain's formula o"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1505.04740","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-05-18T18:00:21Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"a1bb029698468e4b05d0b700483f8e96ac96d8a1bbd3a1bd1eefd41586166a01","abstract_canon_sha256":"50905eec174aa051ba938b2ed1cc4f174aee9b9bded5dba4e5b04dea617f56b6"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:15:38.739461Z","signature_b64":"FJJX1FckMiTKptvky2tGAyVYz+Njw1lvkDdOoenP6diXCickn1KYOg1EqOAARPuDVPhUx3CyCf74yqfkEntCAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bb70b68f898c9fe2470031902f67d699bac9a9127bd4cd42a2abb63532670e1c","last_reissued_at":"2026-05-18T01:15:38.738830Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:15:38.738830Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On Faltings' Delta-Invariant of Hyperelliptic Riemann Surfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.NT","authors_text":"Robert Wilms","submitted_at":"2015-05-18T18:00:21Z","abstract_excerpt":"In this paper we prove new explicit formulas for Faltings' $\\delta$-invariant of an arbitrary hyperelliptic Riemann surface. This has several applications: For example we obtain an explicit lower bound for $\\delta$ depending only on the genus, and we deduce new explicit bounds for the Arakelov self-intersection number $\\omega^2$ associated to hyperelliptic curves over number fields. Furthermore, we obtain an improved version of Szpiro's small points conjecture for hyperelliptic curves of genus at least $3$. Our method allows us in addition to establish a generalization of Rosenhain's formula o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.04740","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1505.04740","created_at":"2026-05-18T01:15:38.738933+00:00"},{"alias_kind":"arxiv_version","alias_value":"1505.04740v2","created_at":"2026-05-18T01:15:38.738933+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1505.04740","created_at":"2026-05-18T01:15:38.738933+00:00"},{"alias_kind":"pith_short_12","alias_value":"XNYLND4JRSP6","created_at":"2026-05-18T12:29:50.041715+00:00"},{"alias_kind":"pith_short_16","alias_value":"XNYLND4JRSP6ERYA","created_at":"2026-05-18T12:29:50.041715+00:00"},{"alias_kind":"pith_short_8","alias_value":"XNYLND4J","created_at":"2026-05-18T12:29:50.041715+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/XNYLND4JRSP6ERYAGGIC6Z6WTG","json":"https://pith.science/pith/XNYLND4JRSP6ERYAGGIC6Z6WTG.json","graph_json":"https://pith.science/api/pith-number/XNYLND4JRSP6ERYAGGIC6Z6WTG/graph.json","events_json":"https://pith.science/api/pith-number/XNYLND4JRSP6ERYAGGIC6Z6WTG/events.json","paper":"https://pith.science/paper/XNYLND4J"},"agent_actions":{"view_html":"https://pith.science/pith/XNYLND4JRSP6ERYAGGIC6Z6WTG","download_json":"https://pith.science/pith/XNYLND4JRSP6ERYAGGIC6Z6WTG.json","view_paper":"https://pith.science/paper/XNYLND4J","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1505.04740&json=true","fetch_graph":"https://pith.science/api/pith-number/XNYLND4JRSP6ERYAGGIC6Z6WTG/graph.json","fetch_events":"https://pith.science/api/pith-number/XNYLND4JRSP6ERYAGGIC6Z6WTG/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/XNYLND4JRSP6ERYAGGIC6Z6WTG/action/timestamp_anchor","attest_storage":"https://pith.science/pith/XNYLND4JRSP6ERYAGGIC6Z6WTG/action/storage_attestation","attest_author":"https://pith.science/pith/XNYLND4JRSP6ERYAGGIC6Z6WTG/action/author_attestation","sign_citation":"https://pith.science/pith/XNYLND4JRSP6ERYAGGIC6Z6WTG/action/citation_signature","submit_replication":"https://pith.science/pith/XNYLND4JRSP6ERYAGGIC6Z6WTG/action/replication_record"}},"created_at":"2026-05-18T01:15:38.738933+00:00","updated_at":"2026-05-18T01:15:38.738933+00:00"}