{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:PWVB7YOLSSTKVMUDWVGEJ2K66W","short_pith_number":"pith:PWVB7YOL","canonical_record":{"source":{"id":"1603.03453","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-03-10T21:24:55Z","cross_cats_sorted":[],"title_canon_sha256":"306a54ecec48a314a44c5b51fa23f39d958ef58d88a0c2b6a532a770db598bfd","abstract_canon_sha256":"0deeb35e19f61cc331ab7bb099bae29108007ea718b54ea35dc0c488046d9d3f"},"schema_version":"1.0"},"canonical_sha256":"7daa1fe1cb94a6aab283b54c44e95ef5aa21986d90bf2d4e1751680c6c7d40cd","source":{"kind":"arxiv","id":"1603.03453","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1603.03453","created_at":"2026-05-18T01:19:15Z"},{"alias_kind":"arxiv_version","alias_value":"1603.03453v1","created_at":"2026-05-18T01:19:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.03453","created_at":"2026-05-18T01:19:15Z"},{"alias_kind":"pith_short_12","alias_value":"PWVB7YOLSSTK","created_at":"2026-05-18T12:30:39Z"},{"alias_kind":"pith_short_16","alias_value":"PWVB7YOLSSTKVMUD","created_at":"2026-05-18T12:30:39Z"},{"alias_kind":"pith_short_8","alias_value":"PWVB7YOL","created_at":"2026-05-18T12:30:39Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:PWVB7YOLSSTKVMUDWVGEJ2K66W","target":"record","payload":{"canonical_record":{"source":{"id":"1603.03453","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-03-10T21:24:55Z","cross_cats_sorted":[],"title_canon_sha256":"306a54ecec48a314a44c5b51fa23f39d958ef58d88a0c2b6a532a770db598bfd","abstract_canon_sha256":"0deeb35e19f61cc331ab7bb099bae29108007ea718b54ea35dc0c488046d9d3f"},"schema_version":"1.0"},"canonical_sha256":"7daa1fe1cb94a6aab283b54c44e95ef5aa21986d90bf2d4e1751680c6c7d40cd","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:19:15.593813Z","signature_b64":"zT9pxKneGqVYd2kMe5WBdajlkCBkkOn+1tMMaDJ4pUIY4YFaW96Yrjo1kocsuhLjxkT/PJvt4zJc4DH639IBCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7daa1fe1cb94a6aab283b54c44e95ef5aa21986d90bf2d4e1751680c6c7d40cd","last_reissued_at":"2026-05-18T01:19:15.593466Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:19:15.593466Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1603.03453","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:19:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Fsew0gzHhHyeNcx8P1k55ZWMLnjj/WRa++b8pzs1poI3/L9lWvgGTYwRxZ0kTVSHwqYKkJiU72FUojpvMbEfAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T20:55:22.018638Z"},"content_sha256":"5a493f7eee49f624f336e5210995122b09c115327ee4683d741450c7d16d7255","schema_version":"1.0","event_id":"sha256:5a493f7eee49f624f336e5210995122b09c115327ee4683d741450c7d16d7255"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:PWVB7YOLSSTKVMUDWVGEJ2K66W","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The $Q_k$ flow on complete non-compact graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Kyeongsu Choi, Panagiota Daskalopoulos","submitted_at":"2016-03-10T21:24:55Z","abstract_excerpt":"We consider the $Q_k$ flow on complete non-compact graphs. We prove that a complete graph evolves by the $Q_k$ curvature up to some time $T$ depending on the radius of a sphere enclosed by the initial graph."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.03453","kind":"arxiv","version":1},"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":"2026-05-18T01:19:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PiU02s4L8RXnMf0KQXY/qwK0n8iaAdA682ojQWSUsekpcOAH9ePXNelgNnYGgRWP9PN/2PNA5EqBE1Bk0EynAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T20:55:22.019288Z"},"content_sha256":"c1628a7a04e2aed57c40910b264a3ba38d483a88d5c4d883680d434e75ba7b9c","schema_version":"1.0","event_id":"sha256:c1628a7a04e2aed57c40910b264a3ba38d483a88d5c4d883680d434e75ba7b9c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/PWVB7YOLSSTKVMUDWVGEJ2K66W/bundle.json","state_url":"https://pith.science/pith/PWVB7YOLSSTKVMUDWVGEJ2K66W/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/PWVB7YOLSSTKVMUDWVGEJ2K66W/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":"2026-06-06T20:55:22Z","links":{"resolver":"https://pith.science/pith/PWVB7YOLSSTKVMUDWVGEJ2K66W","bundle":"https://pith.science/pith/PWVB7YOLSSTKVMUDWVGEJ2K66W/bundle.json","state":"https://pith.science/pith/PWVB7YOLSSTKVMUDWVGEJ2K66W/state.json","well_known_bundle":"https://pith.science/.well-known/pith/PWVB7YOLSSTKVMUDWVGEJ2K66W/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:PWVB7YOLSSTKVMUDWVGEJ2K66W","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":"0deeb35e19f61cc331ab7bb099bae29108007ea718b54ea35dc0c488046d9d3f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-03-10T21:24:55Z","title_canon_sha256":"306a54ecec48a314a44c5b51fa23f39d958ef58d88a0c2b6a532a770db598bfd"},"schema_version":"1.0","source":{"id":"1603.03453","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1603.03453","created_at":"2026-05-18T01:19:15Z"},{"alias_kind":"arxiv_version","alias_value":"1603.03453v1","created_at":"2026-05-18T01:19:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.03453","created_at":"2026-05-18T01:19:15Z"},{"alias_kind":"pith_short_12","alias_value":"PWVB7YOLSSTK","created_at":"2026-05-18T12:30:39Z"},{"alias_kind":"pith_short_16","alias_value":"PWVB7YOLSSTKVMUD","created_at":"2026-05-18T12:30:39Z"},{"alias_kind":"pith_short_8","alias_value":"PWVB7YOL","created_at":"2026-05-18T12:30:39Z"}],"graph_snapshots":[{"event_id":"sha256:c1628a7a04e2aed57c40910b264a3ba38d483a88d5c4d883680d434e75ba7b9c","target":"graph","created_at":"2026-05-18T01:19:15Z","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 consider the $Q_k$ flow on complete non-compact graphs. We prove that a complete graph evolves by the $Q_k$ curvature up to some time $T$ depending on the radius of a sphere enclosed by the initial graph.","authors_text":"Kyeongsu Choi, Panagiota Daskalopoulos","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-03-10T21:24:55Z","title":"The $Q_k$ flow on complete non-compact graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.03453","kind":"arxiv","version":1},"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":"sha256:5a493f7eee49f624f336e5210995122b09c115327ee4683d741450c7d16d7255","target":"record","created_at":"2026-05-18T01:19:15Z","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":"0deeb35e19f61cc331ab7bb099bae29108007ea718b54ea35dc0c488046d9d3f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-03-10T21:24:55Z","title_canon_sha256":"306a54ecec48a314a44c5b51fa23f39d958ef58d88a0c2b6a532a770db598bfd"},"schema_version":"1.0","source":{"id":"1603.03453","kind":"arxiv","version":1}},"canonical_sha256":"7daa1fe1cb94a6aab283b54c44e95ef5aa21986d90bf2d4e1751680c6c7d40cd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7daa1fe1cb94a6aab283b54c44e95ef5aa21986d90bf2d4e1751680c6c7d40cd","first_computed_at":"2026-05-18T01:19:15.593466Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:19:15.593466Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"zT9pxKneGqVYd2kMe5WBdajlkCBkkOn+1tMMaDJ4pUIY4YFaW96Yrjo1kocsuhLjxkT/PJvt4zJc4DH639IBCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:19:15.593813Z","signed_message":"canonical_sha256_bytes"},"source_id":"1603.03453","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5a493f7eee49f624f336e5210995122b09c115327ee4683d741450c7d16d7255","sha256:c1628a7a04e2aed57c40910b264a3ba38d483a88d5c4d883680d434e75ba7b9c"],"state_sha256":"ad826b025ad4e2736d2f21add27307467f6e2516f7835eaddddb96883680b466"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0OEY8ldz1jsbdinkrXhXpicInQauodEmnxu3b6RMOOsxkV/yYHf2v/rxHsah6YszrQqkKElqdTmPOkfrei2bDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-06T20:55:22.023102Z","bundle_sha256":"ecccde70cf2192a58560a1b0628b406323d76e62ee41cc30a41213ebaf1c7483"}}