{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:QGXQHZNURPVLJ7BAGIEHPGTSZZ","short_pith_number":"pith:QGXQHZNU","canonical_record":{"source":{"id":"1312.6388","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-12-22T14:35:27Z","cross_cats_sorted":["math.KT"],"title_canon_sha256":"13ad915c3226e211de64438b82813fe4815ac036e055ce8e31ba46df6b5908ff","abstract_canon_sha256":"1a08ec8f1836126fc9e16822756604ec46f86c2d92f1312a7e66f8607cf6780e"},"schema_version":"1.0"},"canonical_sha256":"81af03e5b48beab4fc203208779a72ce6187e2087f06c57804f208f99e7f3072","source":{"kind":"arxiv","id":"1312.6388","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1312.6388","created_at":"2026-05-18T01:03:06Z"},{"alias_kind":"arxiv_version","alias_value":"1312.6388v3","created_at":"2026-05-18T01:03:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1312.6388","created_at":"2026-05-18T01:03:06Z"},{"alias_kind":"pith_short_12","alias_value":"QGXQHZNURPVL","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_16","alias_value":"QGXQHZNURPVLJ7BA","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_8","alias_value":"QGXQHZNU","created_at":"2026-05-18T12:27:57Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:QGXQHZNURPVLJ7BAGIEHPGTSZZ","target":"record","payload":{"canonical_record":{"source":{"id":"1312.6388","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-12-22T14:35:27Z","cross_cats_sorted":["math.KT"],"title_canon_sha256":"13ad915c3226e211de64438b82813fe4815ac036e055ce8e31ba46df6b5908ff","abstract_canon_sha256":"1a08ec8f1836126fc9e16822756604ec46f86c2d92f1312a7e66f8607cf6780e"},"schema_version":"1.0"},"canonical_sha256":"81af03e5b48beab4fc203208779a72ce6187e2087f06c57804f208f99e7f3072","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:03:06.742586Z","signature_b64":"hYNcPXuvNlDx0GRK1iZyUWFytRkEFiAbdnNesyWcg0A+WijULrI4Y9TLbiriHNezqN3CjbqcgST/xqGOrWWFBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"81af03e5b48beab4fc203208779a72ce6187e2087f06c57804f208f99e7f3072","last_reissued_at":"2026-05-18T01:03:06.742169Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:03:06.742169Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1312.6388","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:03:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HXy8FFwqd1VHcZAU8jGCSkqsQ9Z+q+QYS/w2lD06WXa4tFvac/aL5y+zpkmKpC/G8+Muorx0+hl4PjrTI/gfAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T06:59:29.228577Z"},"content_sha256":"2480e22897b5d24697e570a6e2d0d529c2de7d03413dca79fd8a5df74944c64a","schema_version":"1.0","event_id":"sha256:2480e22897b5d24697e570a6e2d0d529c2de7d03413dca79fd8a5df74944c64a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:QGXQHZNURPVLJ7BAGIEHPGTSZZ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A^1-connected components of schemes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.KT"],"primary_cat":"math.AG","authors_text":"Amit Hogadi, Anand Sawant, Chetan Balwe","submitted_at":"2013-12-22T14:35:27Z","abstract_excerpt":"A conjecture of Morel asserts that the sheaf of A^1-connected components of a simplicial sheaf X is A^1-invariant. A conjecture of Asok-Morel asserts that A^1-connected components of smooth k-schemes coincide with their A^1-chain-connected components and are birational invariants of smooth proper schemes. In this article, we exhibit examples of schemes for which Asok-Morel's conjectures fail to hold and whose Sing_* is not A^1-local. We also give equivalent conditions for Morel's conjecture to hold. A method suggested by these results is then used to prove Morel's conjecture for non-uniruled s"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.6388","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:03:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"05yusv9zOfoMlVFm3HRTcYLXG7Evi0slH9kZjhXrN6Di1PkFsc0oXqZjbJPbf7tdJ0CdEC2zQoQWgPhlxxCnCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T06:59:29.229278Z"},"content_sha256":"5ea46d1a2803c81411305a58427d60fd750f1601e76d853972cad0c24e385823","schema_version":"1.0","event_id":"sha256:5ea46d1a2803c81411305a58427d60fd750f1601e76d853972cad0c24e385823"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QGXQHZNURPVLJ7BAGIEHPGTSZZ/bundle.json","state_url":"https://pith.science/pith/QGXQHZNURPVLJ7BAGIEHPGTSZZ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QGXQHZNURPVLJ7BAGIEHPGTSZZ/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":"2026-06-09T06:59:29Z","links":{"resolver":"https://pith.science/pith/QGXQHZNURPVLJ7BAGIEHPGTSZZ","bundle":"https://pith.science/pith/QGXQHZNURPVLJ7BAGIEHPGTSZZ/bundle.json","state":"https://pith.science/pith/QGXQHZNURPVLJ7BAGIEHPGTSZZ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QGXQHZNURPVLJ7BAGIEHPGTSZZ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:QGXQHZNURPVLJ7BAGIEHPGTSZZ","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":"1a08ec8f1836126fc9e16822756604ec46f86c2d92f1312a7e66f8607cf6780e","cross_cats_sorted":["math.KT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-12-22T14:35:27Z","title_canon_sha256":"13ad915c3226e211de64438b82813fe4815ac036e055ce8e31ba46df6b5908ff"},"schema_version":"1.0","source":{"id":"1312.6388","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1312.6388","created_at":"2026-05-18T01:03:06Z"},{"alias_kind":"arxiv_version","alias_value":"1312.6388v3","created_at":"2026-05-18T01:03:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1312.6388","created_at":"2026-05-18T01:03:06Z"},{"alias_kind":"pith_short_12","alias_value":"QGXQHZNURPVL","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_16","alias_value":"QGXQHZNURPVLJ7BA","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_8","alias_value":"QGXQHZNU","created_at":"2026-05-18T12:27:57Z"}],"graph_snapshots":[{"event_id":"sha256:5ea46d1a2803c81411305a58427d60fd750f1601e76d853972cad0c24e385823","target":"graph","created_at":"2026-05-18T01:03:06Z","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 conjecture of Morel asserts that the sheaf of A^1-connected components of a simplicial sheaf X is A^1-invariant. A conjecture of Asok-Morel asserts that A^1-connected components of smooth k-schemes coincide with their A^1-chain-connected components and are birational invariants of smooth proper schemes. In this article, we exhibit examples of schemes for which Asok-Morel's conjectures fail to hold and whose Sing_* is not A^1-local. We also give equivalent conditions for Morel's conjecture to hold. A method suggested by these results is then used to prove Morel's conjecture for non-uniruled s","authors_text":"Amit Hogadi, Anand Sawant, Chetan Balwe","cross_cats":["math.KT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-12-22T14:35:27Z","title":"A^1-connected components of schemes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.6388","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":"sha256:2480e22897b5d24697e570a6e2d0d529c2de7d03413dca79fd8a5df74944c64a","target":"record","created_at":"2026-05-18T01:03:06Z","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":"1a08ec8f1836126fc9e16822756604ec46f86c2d92f1312a7e66f8607cf6780e","cross_cats_sorted":["math.KT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-12-22T14:35:27Z","title_canon_sha256":"13ad915c3226e211de64438b82813fe4815ac036e055ce8e31ba46df6b5908ff"},"schema_version":"1.0","source":{"id":"1312.6388","kind":"arxiv","version":3}},"canonical_sha256":"81af03e5b48beab4fc203208779a72ce6187e2087f06c57804f208f99e7f3072","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"81af03e5b48beab4fc203208779a72ce6187e2087f06c57804f208f99e7f3072","first_computed_at":"2026-05-18T01:03:06.742169Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:03:06.742169Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"hYNcPXuvNlDx0GRK1iZyUWFytRkEFiAbdnNesyWcg0A+WijULrI4Y9TLbiriHNezqN3CjbqcgST/xqGOrWWFBg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:03:06.742586Z","signed_message":"canonical_sha256_bytes"},"source_id":"1312.6388","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2480e22897b5d24697e570a6e2d0d529c2de7d03413dca79fd8a5df74944c64a","sha256:5ea46d1a2803c81411305a58427d60fd750f1601e76d853972cad0c24e385823"],"state_sha256":"bc998c037eed9ecdb810f62605755315a2c579e9662110dded79a5f64f946814"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"N3Gala48yfob0Qkyd5jL8FHU3puJZxezYQsSdP1skoIhr0GtooLboSemQlAIs4VbBZ4tdXNXzofDsaNPh5QZBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T06:59:29.233048Z","bundle_sha256":"e4c5923072ff942e9e0c5389793f9f54f76f4ae7d6afaee88a68ba157ecca6c0"}}