{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2003:ZWSPG3YW3WRALOCPGPZINGSYI6","short_pith_number":"pith:ZWSPG3YW","canonical_record":{"source":{"id":"math/0305140","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2003-05-09T14:08:47Z","cross_cats_sorted":[],"title_canon_sha256":"98f97d2de75c32ce898882cf1295d36bf834b221476a6609d5ad2d5794d8dc89","abstract_canon_sha256":"d3f9bfa081456836272a5b027c32799432031bccbd34ebe2ad39af3a7131bf9d"},"schema_version":"1.0"},"canonical_sha256":"cda4f36f16dda205b84f33f2869a5847af0e5c8f723738a48df4e6a7065f18dc","source":{"kind":"arxiv","id":"math/0305140","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0305140","created_at":"2026-05-17T23:56:49Z"},{"alias_kind":"arxiv_version","alias_value":"math/0305140v2","created_at":"2026-05-17T23:56:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0305140","created_at":"2026-05-17T23:56:49Z"},{"alias_kind":"pith_short_12","alias_value":"ZWSPG3YW3WRA","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_16","alias_value":"ZWSPG3YW3WRALOCP","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_8","alias_value":"ZWSPG3YW","created_at":"2026-05-18T12:25:52Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2003:ZWSPG3YW3WRALOCPGPZINGSYI6","target":"record","payload":{"canonical_record":{"source":{"id":"math/0305140","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2003-05-09T14:08:47Z","cross_cats_sorted":[],"title_canon_sha256":"98f97d2de75c32ce898882cf1295d36bf834b221476a6609d5ad2d5794d8dc89","abstract_canon_sha256":"d3f9bfa081456836272a5b027c32799432031bccbd34ebe2ad39af3a7131bf9d"},"schema_version":"1.0"},"canonical_sha256":"cda4f36f16dda205b84f33f2869a5847af0e5c8f723738a48df4e6a7065f18dc","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:56:49.242465Z","signature_b64":"L8glLSHunJWvbbzGAk+7yLK4u7sy26IecngXaJL7iHlvn7IfP8G8eEK6+6pL+i3txC9JvZr1h3a9ZlKAMkIzDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cda4f36f16dda205b84f33f2869a5847af0e5c8f723738a48df4e6a7065f18dc","last_reissued_at":"2026-05-17T23:56:49.241859Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:56:49.241859Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math/0305140","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":"2026-05-17T23:56:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cIMeYCm1lvg6JJAgm9nFXfbzmRTHdb/2+yEjYWJFNZXhsqiyfyNuyo3m6CPs3yYZkG0bCwusk0ldv9XkthQzAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T19:12:32.934441Z"},"content_sha256":"4c826dfebd8d8737ae028f3f26d98edd105d8677f71a485f3863e00ba0bbcc02","schema_version":"1.0","event_id":"sha256:4c826dfebd8d8737ae028f3f26d98edd105d8677f71a485f3863e00ba0bbcc02"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2003:ZWSPG3YW3WRALOCPGPZINGSYI6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Eigenvalue estimates for the Dirac operator and harmonic 1-forms of constant length","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Andrei Moroianu, Liviu Ornea","submitted_at":"2003-05-09T14:08:47Z","abstract_excerpt":"We prove that on a compact $n$-dimensional spin manifold admitting a non-trivial harmonic 1-form of constant length, every eigenvalue $\\lambda$ of the Dirac operator satisfies the inequality $\\lambda^2 \\geq \\frac{n-1}{4(n-2)}\\inf_M Scal$. In the limiting case the universal cover of the manifold is isometric to $R\\times N$ where $N$ is a manifold admitting Killing spinors."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0305140","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":"2026-05-17T23:56:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ObvZbcUGw2mPFJMXedrYjJBhDYWuMnTTEWqEC1/v5ZrjcDqQat/nQ+bNy34TbfJNEvJcC9+acbrCPHiIQq+HAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T19:12:32.935285Z"},"content_sha256":"8e62b71a621021cdc1d88e789b074e29e409280b70b051d4acd19206347148f3","schema_version":"1.0","event_id":"sha256:8e62b71a621021cdc1d88e789b074e29e409280b70b051d4acd19206347148f3"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ZWSPG3YW3WRALOCPGPZINGSYI6/bundle.json","state_url":"https://pith.science/pith/ZWSPG3YW3WRALOCPGPZINGSYI6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ZWSPG3YW3WRALOCPGPZINGSYI6/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":"2026-05-26T19:12:32Z","links":{"resolver":"https://pith.science/pith/ZWSPG3YW3WRALOCPGPZINGSYI6","bundle":"https://pith.science/pith/ZWSPG3YW3WRALOCPGPZINGSYI6/bundle.json","state":"https://pith.science/pith/ZWSPG3YW3WRALOCPGPZINGSYI6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ZWSPG3YW3WRALOCPGPZINGSYI6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2003:ZWSPG3YW3WRALOCPGPZINGSYI6","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":"d3f9bfa081456836272a5b027c32799432031bccbd34ebe2ad39af3a7131bf9d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2003-05-09T14:08:47Z","title_canon_sha256":"98f97d2de75c32ce898882cf1295d36bf834b221476a6609d5ad2d5794d8dc89"},"schema_version":"1.0","source":{"id":"math/0305140","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0305140","created_at":"2026-05-17T23:56:49Z"},{"alias_kind":"arxiv_version","alias_value":"math/0305140v2","created_at":"2026-05-17T23:56:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0305140","created_at":"2026-05-17T23:56:49Z"},{"alias_kind":"pith_short_12","alias_value":"ZWSPG3YW3WRA","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_16","alias_value":"ZWSPG3YW3WRALOCP","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_8","alias_value":"ZWSPG3YW","created_at":"2026-05-18T12:25:52Z"}],"graph_snapshots":[{"event_id":"sha256:8e62b71a621021cdc1d88e789b074e29e409280b70b051d4acd19206347148f3","target":"graph","created_at":"2026-05-17T23:56:49Z","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 prove that on a compact $n$-dimensional spin manifold admitting a non-trivial harmonic 1-form of constant length, every eigenvalue $\\lambda$ of the Dirac operator satisfies the inequality $\\lambda^2 \\geq \\frac{n-1}{4(n-2)}\\inf_M Scal$. In the limiting case the universal cover of the manifold is isometric to $R\\times N$ where $N$ is a manifold admitting Killing spinors.","authors_text":"Andrei Moroianu, Liviu Ornea","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2003-05-09T14:08:47Z","title":"Eigenvalue estimates for the Dirac operator and harmonic 1-forms of constant length"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0305140","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":"sha256:4c826dfebd8d8737ae028f3f26d98edd105d8677f71a485f3863e00ba0bbcc02","target":"record","created_at":"2026-05-17T23:56:49Z","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":"d3f9bfa081456836272a5b027c32799432031bccbd34ebe2ad39af3a7131bf9d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2003-05-09T14:08:47Z","title_canon_sha256":"98f97d2de75c32ce898882cf1295d36bf834b221476a6609d5ad2d5794d8dc89"},"schema_version":"1.0","source":{"id":"math/0305140","kind":"arxiv","version":2}},"canonical_sha256":"cda4f36f16dda205b84f33f2869a5847af0e5c8f723738a48df4e6a7065f18dc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cda4f36f16dda205b84f33f2869a5847af0e5c8f723738a48df4e6a7065f18dc","first_computed_at":"2026-05-17T23:56:49.241859Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:56:49.241859Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"L8glLSHunJWvbbzGAk+7yLK4u7sy26IecngXaJL7iHlvn7IfP8G8eEK6+6pL+i3txC9JvZr1h3a9ZlKAMkIzDA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:56:49.242465Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0305140","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4c826dfebd8d8737ae028f3f26d98edd105d8677f71a485f3863e00ba0bbcc02","sha256:8e62b71a621021cdc1d88e789b074e29e409280b70b051d4acd19206347148f3"],"state_sha256":"46037b11dbd2c42a9e2b6ac292f55080176121c02a5b484f4e5ca295afdedac4"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"z0qYuaKgb24I3nR9Cv0HBvdAlhFB0DR/4qAi+AkqyYx4L8wJUkWXXGFlmwN8D3XJhGkrDoqI+u+RYiEnGuQMBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T19:12:32.938867Z","bundle_sha256":"a9c99eef34c96509f82a1ffc7d8ab7fe1ac25359623922a820f46c3bc1a35c7d"}}