{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:6LRQHFFATCTITUZKNCBP3LNPZH","short_pith_number":"pith:6LRQHFFA","schema_version":"1.0","canonical_sha256":"f2e30394a098a689d32a6882fdadafc9cfe67f72380e48a52a871f0f42ad961e","source":{"kind":"arxiv","id":"1505.00602","version":3},"attestation_state":"computed","paper":{"title":"A Gap in the Spectrum of the Faltings Height","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.NT","authors_text":"Steffen L\\\"obrich","submitted_at":"2015-05-04T12:01:10Z","abstract_excerpt":"We show that the minimum $h_{\\text{min}}$ of the stable Faltings height on elliptic curves found by Deligne is followed by a gap. This means that there is a constant $C >0$ such that for every elliptic curve $E/K$ with everywhere semistable reduction over a number field $K$, we either have $h(E/K)=h_{\\text{min}}$ or $h(E/K)\\geq h_{\\text{min}} +C$. We determine such an absolute constant explicitly. On the contrary, we show that there is no such gap for elliptic curves with unstable reduction."},"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":"1505.00602","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-05-04T12:01:10Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"fd5be4a5ccf2d70a70fc2a52b73d6ea90bb94158dea4b190eddb483cea461ec2","abstract_canon_sha256":"e1a6410e83e456d242a75dc645f88f7d185ffd8a07f15d20debe5c094afd66d5"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:24:14.542224Z","signature_b64":"69GJqd/BV4r2BYw5NtdjA8y2BUBxcfXuqsrj+CU/DxbLPBYXQ41VDBtH+DQtRpI0EDaGRz5QnnDbwwtCsBVcDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f2e30394a098a689d32a6882fdadafc9cfe67f72380e48a52a871f0f42ad961e","last_reissued_at":"2026-05-18T01:24:14.541679Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:24:14.541679Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A Gap in the Spectrum of the Faltings Height","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.NT","authors_text":"Steffen L\\\"obrich","submitted_at":"2015-05-04T12:01:10Z","abstract_excerpt":"We show that the minimum $h_{\\text{min}}$ of the stable Faltings height on elliptic curves found by Deligne is followed by a gap. This means that there is a constant $C >0$ such that for every elliptic curve $E/K$ with everywhere semistable reduction over a number field $K$, we either have $h(E/K)=h_{\\text{min}}$ or $h(E/K)\\geq h_{\\text{min}} +C$. We determine such an absolute constant explicitly. On the contrary, we show that there is no such gap for elliptic curves with unstable reduction."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.00602","kind":"arxiv","version":3},"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":"1505.00602","created_at":"2026-05-18T01:24:14.541763+00:00"},{"alias_kind":"arxiv_version","alias_value":"1505.00602v3","created_at":"2026-05-18T01:24:14.541763+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1505.00602","created_at":"2026-05-18T01:24:14.541763+00:00"},{"alias_kind":"pith_short_12","alias_value":"6LRQHFFATCTI","created_at":"2026-05-18T12:29:07.941421+00:00"},{"alias_kind":"pith_short_16","alias_value":"6LRQHFFATCTITUZK","created_at":"2026-05-18T12:29:07.941421+00:00"},{"alias_kind":"pith_short_8","alias_value":"6LRQHFFA","created_at":"2026-05-18T12:29:07.941421+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/6LRQHFFATCTITUZKNCBP3LNPZH","json":"https://pith.science/pith/6LRQHFFATCTITUZKNCBP3LNPZH.json","graph_json":"https://pith.science/api/pith-number/6LRQHFFATCTITUZKNCBP3LNPZH/graph.json","events_json":"https://pith.science/api/pith-number/6LRQHFFATCTITUZKNCBP3LNPZH/events.json","paper":"https://pith.science/paper/6LRQHFFA"},"agent_actions":{"view_html":"https://pith.science/pith/6LRQHFFATCTITUZKNCBP3LNPZH","download_json":"https://pith.science/pith/6LRQHFFATCTITUZKNCBP3LNPZH.json","view_paper":"https://pith.science/paper/6LRQHFFA","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1505.00602&json=true","fetch_graph":"https://pith.science/api/pith-number/6LRQHFFATCTITUZKNCBP3LNPZH/graph.json","fetch_events":"https://pith.science/api/pith-number/6LRQHFFATCTITUZKNCBP3LNPZH/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/6LRQHFFATCTITUZKNCBP3LNPZH/action/timestamp_anchor","attest_storage":"https://pith.science/pith/6LRQHFFATCTITUZKNCBP3LNPZH/action/storage_attestation","attest_author":"https://pith.science/pith/6LRQHFFATCTITUZKNCBP3LNPZH/action/author_attestation","sign_citation":"https://pith.science/pith/6LRQHFFATCTITUZKNCBP3LNPZH/action/citation_signature","submit_replication":"https://pith.science/pith/6LRQHFFATCTITUZKNCBP3LNPZH/action/replication_record"}},"created_at":"2026-05-18T01:24:14.541763+00:00","updated_at":"2026-05-18T01:24:14.541763+00:00"}