{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2009:XHECQA6HQWPCC3GIBAHYRNQBLH","short_pith_number":"pith:XHECQA6H","canonical_record":{"source":{"id":"0912.0421","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2009-12-02T19:06:11Z","cross_cats_sorted":[],"title_canon_sha256":"c7ad6e1f5e83231273c5e9a442ee91e51ce619566e117f6762faa3555e7f01e9","abstract_canon_sha256":"a1e97705943ea356146418b44c954d6865848d6c4f50d927a31a48aaee99db76"},"schema_version":"1.0"},"canonical_sha256":"b9c82803c7859e216cc8080f88b60159e2131c12858fa37c95d2c354afa3a7fa","source":{"kind":"arxiv","id":"0912.0421","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0912.0421","created_at":"2026-05-18T03:40:16Z"},{"alias_kind":"arxiv_version","alias_value":"0912.0421v3","created_at":"2026-05-18T03:40:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0912.0421","created_at":"2026-05-18T03:40:16Z"},{"alias_kind":"pith_short_12","alias_value":"XHECQA6HQWPC","created_at":"2026-05-18T12:26:02Z"},{"alias_kind":"pith_short_16","alias_value":"XHECQA6HQWPCC3GI","created_at":"2026-05-18T12:26:02Z"},{"alias_kind":"pith_short_8","alias_value":"XHECQA6H","created_at":"2026-05-18T12:26:02Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2009:XHECQA6HQWPCC3GIBAHYRNQBLH","target":"record","payload":{"canonical_record":{"source":{"id":"0912.0421","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2009-12-02T19:06:11Z","cross_cats_sorted":[],"title_canon_sha256":"c7ad6e1f5e83231273c5e9a442ee91e51ce619566e117f6762faa3555e7f01e9","abstract_canon_sha256":"a1e97705943ea356146418b44c954d6865848d6c4f50d927a31a48aaee99db76"},"schema_version":"1.0"},"canonical_sha256":"b9c82803c7859e216cc8080f88b60159e2131c12858fa37c95d2c354afa3a7fa","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:40:16.556068Z","signature_b64":"0IyMDhJ0CIZCfn0lvj8RDQn2ipuJZTShZ6X0mQ+BASK/+HJN+6V5G0G4UYzmJhKsA0KgMJTEmJSxfsc3LWSNAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b9c82803c7859e216cc8080f88b60159e2131c12858fa37c95d2c354afa3a7fa","last_reissued_at":"2026-05-18T03:40:16.555408Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:40:16.555408Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0912.0421","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":"2026-05-18T03:40:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FsbPfvXxzGNDTZdJsVpZk7qTkXLZ0c+bFGutFAJSeHi5PorKDZRMSHCAZp/G7Vg94jjHcQmgBMSnPKLqiIGuBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T18:24:07.268569Z"},"content_sha256":"e91bd5d857ffdf27461e01222532e224a13eb4f2e7f024b70c5d7f9fba2ae315","schema_version":"1.0","event_id":"sha256:e91bd5d857ffdf27461e01222532e224a13eb4f2e7f024b70c5d7f9fba2ae315"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2009:XHECQA6HQWPCC3GIBAHYRNQBLH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A heat flow for special metrics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Frederik Witt, Hartmut Weiss","submitted_at":"2009-12-02T19:06:11Z","abstract_excerpt":"On the space of positive 3-forms on a seven-manifold, we study a natural functional whose critical points induce metrics with holonomy contained in $G_2$. We prove short-time existence and uniqueness for its negative gradient flow. Furthermore, we show that the flow exists for all times and converges modulo diffeomorphisms to some critical point for any initial condition sufficiently $C^\\infty$-close to a critical point."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0912.0421","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":"2026-05-18T03:40:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/gj45koHIeWtNjat6zWEP3FaKdAVFgsXpTPorMsj8XUai9ZIOSf1/0yoBuDxz4IlUtqdOW3aHdeJi5Nieh/CAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T18:24:07.268898Z"},"content_sha256":"c04952e9dd7a2fe7ae2c8e2f00958ae65efde4195af70fbfc59110ff59dac848","schema_version":"1.0","event_id":"sha256:c04952e9dd7a2fe7ae2c8e2f00958ae65efde4195af70fbfc59110ff59dac848"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/XHECQA6HQWPCC3GIBAHYRNQBLH/bundle.json","state_url":"https://pith.science/pith/XHECQA6HQWPCC3GIBAHYRNQBLH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/XHECQA6HQWPCC3GIBAHYRNQBLH/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":"2026-06-24T18:24:07Z","links":{"resolver":"https://pith.science/pith/XHECQA6HQWPCC3GIBAHYRNQBLH","bundle":"https://pith.science/pith/XHECQA6HQWPCC3GIBAHYRNQBLH/bundle.json","state":"https://pith.science/pith/XHECQA6HQWPCC3GIBAHYRNQBLH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/XHECQA6HQWPCC3GIBAHYRNQBLH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:XHECQA6HQWPCC3GIBAHYRNQBLH","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":"a1e97705943ea356146418b44c954d6865848d6c4f50d927a31a48aaee99db76","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2009-12-02T19:06:11Z","title_canon_sha256":"c7ad6e1f5e83231273c5e9a442ee91e51ce619566e117f6762faa3555e7f01e9"},"schema_version":"1.0","source":{"id":"0912.0421","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0912.0421","created_at":"2026-05-18T03:40:16Z"},{"alias_kind":"arxiv_version","alias_value":"0912.0421v3","created_at":"2026-05-18T03:40:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0912.0421","created_at":"2026-05-18T03:40:16Z"},{"alias_kind":"pith_short_12","alias_value":"XHECQA6HQWPC","created_at":"2026-05-18T12:26:02Z"},{"alias_kind":"pith_short_16","alias_value":"XHECQA6HQWPCC3GI","created_at":"2026-05-18T12:26:02Z"},{"alias_kind":"pith_short_8","alias_value":"XHECQA6H","created_at":"2026-05-18T12:26:02Z"}],"graph_snapshots":[{"event_id":"sha256:c04952e9dd7a2fe7ae2c8e2f00958ae65efde4195af70fbfc59110ff59dac848","target":"graph","created_at":"2026-05-18T03:40:16Z","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":"On the space of positive 3-forms on a seven-manifold, we study a natural functional whose critical points induce metrics with holonomy contained in $G_2$. We prove short-time existence and uniqueness for its negative gradient flow. Furthermore, we show that the flow exists for all times and converges modulo diffeomorphisms to some critical point for any initial condition sufficiently $C^\\infty$-close to a critical point.","authors_text":"Frederik Witt, Hartmut Weiss","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2009-12-02T19:06:11Z","title":"A heat flow for special metrics"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0912.0421","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:e91bd5d857ffdf27461e01222532e224a13eb4f2e7f024b70c5d7f9fba2ae315","target":"record","created_at":"2026-05-18T03:40:16Z","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":"a1e97705943ea356146418b44c954d6865848d6c4f50d927a31a48aaee99db76","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2009-12-02T19:06:11Z","title_canon_sha256":"c7ad6e1f5e83231273c5e9a442ee91e51ce619566e117f6762faa3555e7f01e9"},"schema_version":"1.0","source":{"id":"0912.0421","kind":"arxiv","version":3}},"canonical_sha256":"b9c82803c7859e216cc8080f88b60159e2131c12858fa37c95d2c354afa3a7fa","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b9c82803c7859e216cc8080f88b60159e2131c12858fa37c95d2c354afa3a7fa","first_computed_at":"2026-05-18T03:40:16.555408Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:40:16.555408Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"0IyMDhJ0CIZCfn0lvj8RDQn2ipuJZTShZ6X0mQ+BASK/+HJN+6V5G0G4UYzmJhKsA0KgMJTEmJSxfsc3LWSNAg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:40:16.556068Z","signed_message":"canonical_sha256_bytes"},"source_id":"0912.0421","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e91bd5d857ffdf27461e01222532e224a13eb4f2e7f024b70c5d7f9fba2ae315","sha256:c04952e9dd7a2fe7ae2c8e2f00958ae65efde4195af70fbfc59110ff59dac848"],"state_sha256":"dab3115c40b2451090dcdbfe3ac26a667d903acca76acd8e07ef48b670396196"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tGliKI5KHczU28wmKC2aoW2bMludY5W+YCPw6eFhWOP5nUriEcrwIJyN95zlLS3kYaK/+t2ilVjW3ItKj23LDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-24T18:24:07.270756Z","bundle_sha256":"1f0c0231f64e709f87aac1ebde295c58efb07fbcce7eb006619200c11467c726"}}