{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2020:I52EKZGJQQBYOGSNSR5VO4PEWH","short_pith_number":"pith:I52EKZGJ","canonical_record":{"source":{"id":"2005.09845","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2020-05-20T05:03:39Z","cross_cats_sorted":[],"title_canon_sha256":"61f5e2a252e53d55de82836ac56e3fd5fc18e0ec3f7a7a193fb0b5c80e7ea6cb","abstract_canon_sha256":"3c03273e2f974dc36641acc27ec90a6287c1df305494c07f06f84a45b3809cae"},"schema_version":"1.0"},"canonical_sha256":"47744564c98403871a4d947b5771e4b1c045c7bd3794493afda55c1bbfc90651","source":{"kind":"arxiv","id":"2005.09845","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2005.09845","created_at":"2026-07-05T01:11:13Z"},{"alias_kind":"arxiv_version","alias_value":"2005.09845v2","created_at":"2026-07-05T01:11:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2005.09845","created_at":"2026-07-05T01:11:13Z"},{"alias_kind":"pith_short_12","alias_value":"I52EKZGJQQBY","created_at":"2026-07-05T01:11:13Z"},{"alias_kind":"pith_short_16","alias_value":"I52EKZGJQQBYOGSN","created_at":"2026-07-05T01:11:13Z"},{"alias_kind":"pith_short_8","alias_value":"I52EKZGJ","created_at":"2026-07-05T01:11:13Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2020:I52EKZGJQQBYOGSNSR5VO4PEWH","target":"record","payload":{"canonical_record":{"source":{"id":"2005.09845","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2020-05-20T05:03:39Z","cross_cats_sorted":[],"title_canon_sha256":"61f5e2a252e53d55de82836ac56e3fd5fc18e0ec3f7a7a193fb0b5c80e7ea6cb","abstract_canon_sha256":"3c03273e2f974dc36641acc27ec90a6287c1df305494c07f06f84a45b3809cae"},"schema_version":"1.0"},"canonical_sha256":"47744564c98403871a4d947b5771e4b1c045c7bd3794493afda55c1bbfc90651","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T01:11:13.912179Z","signature_b64":"akBwZYcg2/fxugmeT8PrI7+X2GJWo/tT8sLnnBliDWFRaOQ6XiHtVSzhl7nIB44P6u7giR/au5d9nv1E0Hr/CQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"47744564c98403871a4d947b5771e4b1c045c7bd3794493afda55c1bbfc90651","last_reissued_at":"2026-07-05T01:11:13.911810Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T01:11:13.911810Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2005.09845","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":"2026-07-05T01:11:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LOl85fAXUchYTYVYEfvag9Zm5/Z0KsyfFW2Mua6PRk3Yre16GVEsuxPA4PxcaxeE1pxX2ug0GtloQzkQcFZiBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-05T13:17:59.015652Z"},"content_sha256":"a87fef1b09271c72e65cce814f4abc73dab88c46502cabc6026a4f996a35d63f","schema_version":"1.0","event_id":"sha256:a87fef1b09271c72e65cce814f4abc73dab88c46502cabc6026a4f996a35d63f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2020:I52EKZGJQQBYOGSNSR5VO4PEWH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On Ecker's local integral quantity at infinity for ancient mean curvature flows","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Keita Kunikawa","submitted_at":"2020-05-20T05:03:39Z","abstract_excerpt":"We point out that Ecker's local integral quantity agrees with Huisken's global integral quantity at infinity for ancient mean curvature flows if Huisken's one is finite on each time-slice. In particular, this means that the finiteness of Ecker's integral quantity at infinity implies the finiteness of the entropy at infinity."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2005.09845","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2005.09845/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T01:11:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dbmTeYtx1aAqXl+RJGe6gjDWIuYNG+yZpLtY8g3DbW1ijURmCyK/x9w5+D8oGXwjwnP1TsHvb6v7Gj/f2ldfAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-05T13:17:59.016324Z"},"content_sha256":"619ac8094bad6edd0810a7ddab88928a520106c92c74e60a0d2ee325d62f3053","schema_version":"1.0","event_id":"sha256:619ac8094bad6edd0810a7ddab88928a520106c92c74e60a0d2ee325d62f3053"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/I52EKZGJQQBYOGSNSR5VO4PEWH/bundle.json","state_url":"https://pith.science/pith/I52EKZGJQQBYOGSNSR5VO4PEWH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/I52EKZGJQQBYOGSNSR5VO4PEWH/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":"2026-07-05T13:17:59Z","links":{"resolver":"https://pith.science/pith/I52EKZGJQQBYOGSNSR5VO4PEWH","bundle":"https://pith.science/pith/I52EKZGJQQBYOGSNSR5VO4PEWH/bundle.json","state":"https://pith.science/pith/I52EKZGJQQBYOGSNSR5VO4PEWH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/I52EKZGJQQBYOGSNSR5VO4PEWH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:I52EKZGJQQBYOGSNSR5VO4PEWH","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":"3c03273e2f974dc36641acc27ec90a6287c1df305494c07f06f84a45b3809cae","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2020-05-20T05:03:39Z","title_canon_sha256":"61f5e2a252e53d55de82836ac56e3fd5fc18e0ec3f7a7a193fb0b5c80e7ea6cb"},"schema_version":"1.0","source":{"id":"2005.09845","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2005.09845","created_at":"2026-07-05T01:11:13Z"},{"alias_kind":"arxiv_version","alias_value":"2005.09845v2","created_at":"2026-07-05T01:11:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2005.09845","created_at":"2026-07-05T01:11:13Z"},{"alias_kind":"pith_short_12","alias_value":"I52EKZGJQQBY","created_at":"2026-07-05T01:11:13Z"},{"alias_kind":"pith_short_16","alias_value":"I52EKZGJQQBYOGSN","created_at":"2026-07-05T01:11:13Z"},{"alias_kind":"pith_short_8","alias_value":"I52EKZGJ","created_at":"2026-07-05T01:11:13Z"}],"graph_snapshots":[{"event_id":"sha256:619ac8094bad6edd0810a7ddab88928a520106c92c74e60a0d2ee325d62f3053","target":"graph","created_at":"2026-07-05T01:11:13Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2005.09845/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We point out that Ecker's local integral quantity agrees with Huisken's global integral quantity at infinity for ancient mean curvature flows if Huisken's one is finite on each time-slice. In particular, this means that the finiteness of Ecker's integral quantity at infinity implies the finiteness of the entropy at infinity.","authors_text":"Keita Kunikawa","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2020-05-20T05:03:39Z","title":"On Ecker's local integral quantity at infinity for ancient mean curvature flows"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2005.09845","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:a87fef1b09271c72e65cce814f4abc73dab88c46502cabc6026a4f996a35d63f","target":"record","created_at":"2026-07-05T01:11:13Z","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":"3c03273e2f974dc36641acc27ec90a6287c1df305494c07f06f84a45b3809cae","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2020-05-20T05:03:39Z","title_canon_sha256":"61f5e2a252e53d55de82836ac56e3fd5fc18e0ec3f7a7a193fb0b5c80e7ea6cb"},"schema_version":"1.0","source":{"id":"2005.09845","kind":"arxiv","version":2}},"canonical_sha256":"47744564c98403871a4d947b5771e4b1c045c7bd3794493afda55c1bbfc90651","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"47744564c98403871a4d947b5771e4b1c045c7bd3794493afda55c1bbfc90651","first_computed_at":"2026-07-05T01:11:13.911810Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T01:11:13.911810Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"akBwZYcg2/fxugmeT8PrI7+X2GJWo/tT8sLnnBliDWFRaOQ6XiHtVSzhl7nIB44P6u7giR/au5d9nv1E0Hr/CQ==","signature_status":"signed_v1","signed_at":"2026-07-05T01:11:13.912179Z","signed_message":"canonical_sha256_bytes"},"source_id":"2005.09845","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a87fef1b09271c72e65cce814f4abc73dab88c46502cabc6026a4f996a35d63f","sha256:619ac8094bad6edd0810a7ddab88928a520106c92c74e60a0d2ee325d62f3053"],"state_sha256":"6a92245fe098cf969901d6cb62ad551c5a8c0b4123aeb731fe4ebb451235d672"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"iGTmH3KJ904waaxIUd0lcCIjeV/KyVe8n0jCB0QRdRX96OISXA6MZaj2tR1/jMSrSRvYLLvohCAmdMEmI3NzAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-05T13:17:59.024239Z","bundle_sha256":"8ae3e3793be0eb1ec1ca5182967123f69e36cdc8b0a04cdb69ffcb29fa9a55b7"}}