{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:MQ4FODDHVHFLEN2IQYKNAB6BPE","short_pith_number":"pith:MQ4FODDH","canonical_record":{"source":{"id":"1109.6705","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-09-30T02:51:47Z","cross_cats_sorted":[],"title_canon_sha256":"c588d74c8938bbf6f3475c0c70c02050de7b6a07377f30e012ff2c154190373a","abstract_canon_sha256":"25a35d5df5d13a49228fd37c00a5da66947df7541569a2264312beb5d08ffe04"},"schema_version":"1.0"},"canonical_sha256":"6438570c67a9cab237488614d007c17907169e6ed69475f9e8d1cacd73d2e237","source":{"kind":"arxiv","id":"1109.6705","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1109.6705","created_at":"2026-05-18T03:06:03Z"},{"alias_kind":"arxiv_version","alias_value":"1109.6705v2","created_at":"2026-05-18T03:06:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1109.6705","created_at":"2026-05-18T03:06:03Z"},{"alias_kind":"pith_short_12","alias_value":"MQ4FODDHVHFL","created_at":"2026-05-18T12:26:34Z"},{"alias_kind":"pith_short_16","alias_value":"MQ4FODDHVHFLEN2I","created_at":"2026-05-18T12:26:34Z"},{"alias_kind":"pith_short_8","alias_value":"MQ4FODDH","created_at":"2026-05-18T12:26:34Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:MQ4FODDHVHFLEN2IQYKNAB6BPE","target":"record","payload":{"canonical_record":{"source":{"id":"1109.6705","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-09-30T02:51:47Z","cross_cats_sorted":[],"title_canon_sha256":"c588d74c8938bbf6f3475c0c70c02050de7b6a07377f30e012ff2c154190373a","abstract_canon_sha256":"25a35d5df5d13a49228fd37c00a5da66947df7541569a2264312beb5d08ffe04"},"schema_version":"1.0"},"canonical_sha256":"6438570c67a9cab237488614d007c17907169e6ed69475f9e8d1cacd73d2e237","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:06:03.878030Z","signature_b64":"SCiiD25lJoN3fhh7dLpbNcfThILhrMKBQvDG51woHIFZI2N1GPuZpQSNzlxMF+3alpqqif1i08f5nLSHe04cBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6438570c67a9cab237488614d007c17907169e6ed69475f9e8d1cacd73d2e237","last_reissued_at":"2026-05-18T03:06:03.877464Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:06:03.877464Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1109.6705","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":"2026-05-18T03:06:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YCURH1SQEVYwST44EOuQQ6L5ZLY+BOSx2f8u8DH9HvkCoAm0Hc2Lv/yPXxikJ2ZeflW3HgNiFKAFGbkOAWUhDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T12:19:04.973822Z"},"content_sha256":"e9a0709bdd6535b1ac9023cb3f680c398091bf7ebb7c9d23cb826be37f7a3cb1","schema_version":"1.0","event_id":"sha256:e9a0709bdd6535b1ac9023cb3f680c398091bf7ebb7c9d23cb826be37f7a3cb1"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:MQ4FODDHVHFLEN2IQYKNAB6BPE","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Rigid curves on $\\bar M_{0,n}$ and arithmetic breaks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Ana-Maria Castravet, Jenia Tevelev","submitted_at":"2011-09-30T02:51:47Z","abstract_excerpt":"A result of Keel and McKernan states that a hypothetical counterexample to the F-conjecture must come from rigid curves on $\\bar {M}_{0,n}$ that intersect the interior. We exhibit several ways of constructing rigid curves. In all our examples, a reduction mod p argument shows that the classes of the rigid curves that we construct can be decomposed as sums of F-curves."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.6705","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":"2026-05-18T03:06:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qXKtCIwv7AEGIglhRutFYYa75KdCof6Dipg9BUd/gvEMd6xNAya4L38rI0CacplUDjybl/bHmPaT26e7QB/cCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T12:19:04.974555Z"},"content_sha256":"f8a9acdb36b7a7c816f36d0a974269adfbf761603165e328e7a1eee9ac8a3b01","schema_version":"1.0","event_id":"sha256:f8a9acdb36b7a7c816f36d0a974269adfbf761603165e328e7a1eee9ac8a3b01"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MQ4FODDHVHFLEN2IQYKNAB6BPE/bundle.json","state_url":"https://pith.science/pith/MQ4FODDHVHFLEN2IQYKNAB6BPE/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MQ4FODDHVHFLEN2IQYKNAB6BPE/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":"2026-05-27T12:19:04Z","links":{"resolver":"https://pith.science/pith/MQ4FODDHVHFLEN2IQYKNAB6BPE","bundle":"https://pith.science/pith/MQ4FODDHVHFLEN2IQYKNAB6BPE/bundle.json","state":"https://pith.science/pith/MQ4FODDHVHFLEN2IQYKNAB6BPE/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MQ4FODDHVHFLEN2IQYKNAB6BPE/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:MQ4FODDHVHFLEN2IQYKNAB6BPE","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":"25a35d5df5d13a49228fd37c00a5da66947df7541569a2264312beb5d08ffe04","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-09-30T02:51:47Z","title_canon_sha256":"c588d74c8938bbf6f3475c0c70c02050de7b6a07377f30e012ff2c154190373a"},"schema_version":"1.0","source":{"id":"1109.6705","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1109.6705","created_at":"2026-05-18T03:06:03Z"},{"alias_kind":"arxiv_version","alias_value":"1109.6705v2","created_at":"2026-05-18T03:06:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1109.6705","created_at":"2026-05-18T03:06:03Z"},{"alias_kind":"pith_short_12","alias_value":"MQ4FODDHVHFL","created_at":"2026-05-18T12:26:34Z"},{"alias_kind":"pith_short_16","alias_value":"MQ4FODDHVHFLEN2I","created_at":"2026-05-18T12:26:34Z"},{"alias_kind":"pith_short_8","alias_value":"MQ4FODDH","created_at":"2026-05-18T12:26:34Z"}],"graph_snapshots":[{"event_id":"sha256:f8a9acdb36b7a7c816f36d0a974269adfbf761603165e328e7a1eee9ac8a3b01","target":"graph","created_at":"2026-05-18T03:06:03Z","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":"A result of Keel and McKernan states that a hypothetical counterexample to the F-conjecture must come from rigid curves on $\\bar {M}_{0,n}$ that intersect the interior. We exhibit several ways of constructing rigid curves. In all our examples, a reduction mod p argument shows that the classes of the rigid curves that we construct can be decomposed as sums of F-curves.","authors_text":"Ana-Maria Castravet, Jenia Tevelev","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-09-30T02:51:47Z","title":"Rigid curves on $\\bar M_{0,n}$ and arithmetic breaks"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.6705","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:e9a0709bdd6535b1ac9023cb3f680c398091bf7ebb7c9d23cb826be37f7a3cb1","target":"record","created_at":"2026-05-18T03:06:03Z","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":"25a35d5df5d13a49228fd37c00a5da66947df7541569a2264312beb5d08ffe04","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-09-30T02:51:47Z","title_canon_sha256":"c588d74c8938bbf6f3475c0c70c02050de7b6a07377f30e012ff2c154190373a"},"schema_version":"1.0","source":{"id":"1109.6705","kind":"arxiv","version":2}},"canonical_sha256":"6438570c67a9cab237488614d007c17907169e6ed69475f9e8d1cacd73d2e237","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6438570c67a9cab237488614d007c17907169e6ed69475f9e8d1cacd73d2e237","first_computed_at":"2026-05-18T03:06:03.877464Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:06:03.877464Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"SCiiD25lJoN3fhh7dLpbNcfThILhrMKBQvDG51woHIFZI2N1GPuZpQSNzlxMF+3alpqqif1i08f5nLSHe04cBw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:06:03.878030Z","signed_message":"canonical_sha256_bytes"},"source_id":"1109.6705","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e9a0709bdd6535b1ac9023cb3f680c398091bf7ebb7c9d23cb826be37f7a3cb1","sha256:f8a9acdb36b7a7c816f36d0a974269adfbf761603165e328e7a1eee9ac8a3b01"],"state_sha256":"6f2df1f924c0e8d6f3da42ef9e247f61f019e38ddb2dc27e391f5fe6b1c2c94a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"T0Ju3NEL53S9Wiz4/8H/yBX9cb5aYdDSs10xjBYZqaFZPBxDLDMESfxafxkIX67L6V4yjzXw/uetG+5RkaV8DA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T12:19:04.978045Z","bundle_sha256":"4179bc8f86a03b68dbc4b98a62994be6b29af8daf7c686cb4461778a3093f748"}}