{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:6LRQHFFATCTITUZKNCBP3LNPZH","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":"e1a6410e83e456d242a75dc645f88f7d185ffd8a07f15d20debe5c094afd66d5","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-05-04T12:01:10Z","title_canon_sha256":"fd5be4a5ccf2d70a70fc2a52b73d6ea90bb94158dea4b190eddb483cea461ec2"},"schema_version":"1.0","source":{"id":"1505.00602","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1505.00602","created_at":"2026-05-18T01:24:14Z"},{"alias_kind":"arxiv_version","alias_value":"1505.00602v3","created_at":"2026-05-18T01:24:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1505.00602","created_at":"2026-05-18T01:24:14Z"},{"alias_kind":"pith_short_12","alias_value":"6LRQHFFATCTI","created_at":"2026-05-18T12:29:07Z"},{"alias_kind":"pith_short_16","alias_value":"6LRQHFFATCTITUZK","created_at":"2026-05-18T12:29:07Z"},{"alias_kind":"pith_short_8","alias_value":"6LRQHFFA","created_at":"2026-05-18T12:29:07Z"}],"graph_snapshots":[{"event_id":"sha256:0769a18c1bb181eab2b6a3ca117bf06f25846e3d46fd68ac71629f10201a9fba","target":"graph","created_at":"2026-05-18T01:24:14Z","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":"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.","authors_text":"Steffen L\\\"obrich","cross_cats":["math.AG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-05-04T12:01:10Z","title":"A Gap in the Spectrum of the Faltings Height"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.00602","kind":"arxiv","version":3},"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:ff4ad2534726cd1964bb96e6f8c622c0c199e670d1839b8fac65f2f190cabdad","target":"record","created_at":"2026-05-18T01:24:14Z","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":"e1a6410e83e456d242a75dc645f88f7d185ffd8a07f15d20debe5c094afd66d5","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-05-04T12:01:10Z","title_canon_sha256":"fd5be4a5ccf2d70a70fc2a52b73d6ea90bb94158dea4b190eddb483cea461ec2"},"schema_version":"1.0","source":{"id":"1505.00602","kind":"arxiv","version":3}},"canonical_sha256":"f2e30394a098a689d32a6882fdadafc9cfe67f72380e48a52a871f0f42ad961e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f2e30394a098a689d32a6882fdadafc9cfe67f72380e48a52a871f0f42ad961e","first_computed_at":"2026-05-18T01:24:14.541679Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:24:14.541679Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"69GJqd/BV4r2BYw5NtdjA8y2BUBxcfXuqsrj+CU/DxbLPBYXQ41VDBtH+DQtRpI0EDaGRz5QnnDbwwtCsBVcDw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:24:14.542224Z","signed_message":"canonical_sha256_bytes"},"source_id":"1505.00602","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ff4ad2534726cd1964bb96e6f8c622c0c199e670d1839b8fac65f2f190cabdad","sha256:0769a18c1bb181eab2b6a3ca117bf06f25846e3d46fd68ac71629f10201a9fba"],"state_sha256":"a17f9168030b7702553fa816a510a4a882d9453acf0169fcfc23c683ed43ba32"}