{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:O54FTOWAVXCL6XVDXTVDCQKPKW","short_pith_number":"pith:O54FTOWA","canonical_record":{"source":{"id":"1409.1525","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2014-09-04T18:47:06Z","cross_cats_sorted":["math-ph","math.AP","math.MP"],"title_canon_sha256":"2683ccdd0dab9b153837f0de2523b01f8cfbb7151e3c47adf58059fd96309cdf","abstract_canon_sha256":"d032d74ab4a45a0864189d0d8e5d43e30a30f8fdbc6969ee1b902c55a5d79881"},"schema_version":"1.0"},"canonical_sha256":"777859bac0adc4bf5ea3bcea31414f55bf63b26223959486dd1f5f9e3cc63af6","source":{"kind":"arxiv","id":"1409.1525","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1409.1525","created_at":"2026-05-18T01:02:14Z"},{"alias_kind":"arxiv_version","alias_value":"1409.1525v4","created_at":"2026-05-18T01:02:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1409.1525","created_at":"2026-05-18T01:02:14Z"},{"alias_kind":"pith_short_12","alias_value":"O54FTOWAVXCL","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_16","alias_value":"O54FTOWAVXCL6XVD","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_8","alias_value":"O54FTOWA","created_at":"2026-05-18T12:28:41Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:O54FTOWAVXCL6XVDXTVDCQKPKW","target":"record","payload":{"canonical_record":{"source":{"id":"1409.1525","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2014-09-04T18:47:06Z","cross_cats_sorted":["math-ph","math.AP","math.MP"],"title_canon_sha256":"2683ccdd0dab9b153837f0de2523b01f8cfbb7151e3c47adf58059fd96309cdf","abstract_canon_sha256":"d032d74ab4a45a0864189d0d8e5d43e30a30f8fdbc6969ee1b902c55a5d79881"},"schema_version":"1.0"},"canonical_sha256":"777859bac0adc4bf5ea3bcea31414f55bf63b26223959486dd1f5f9e3cc63af6","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:02:14.166573Z","signature_b64":"DZJV6XDlgsoM6b30ZtA+0da/2tPi8sVRlPZfeAjsV4pMPQBAtPRPAZWmsczDimHQTz/AMrK4HDFOMU2RLVBuAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"777859bac0adc4bf5ea3bcea31414f55bf63b26223959486dd1f5f9e3cc63af6","last_reissued_at":"2026-05-18T01:02:14.165797Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:02:14.165797Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1409.1525","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:02:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xyepYHYciLgZvanZGWbbmU/FC5vFc6Chznj213gGz0xGta6x0MlUA6XupiBUMWGK+ZUHNwaL4NGeqZFk1unOBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T14:29:50.550794Z"},"content_sha256":"eafa43e39ee386cffc8fc7c6531072eb80a8e751db8cd8a20c8baf309c687910","schema_version":"1.0","event_id":"sha256:eafa43e39ee386cffc8fc7c6531072eb80a8e751db8cd8a20c8baf309c687910"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:O54FTOWAVXCL6XVDXTVDCQKPKW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Global existence and convergence of solutions to gradient systems and applications to Yang-Mills gradient flow","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.AP","math.MP"],"primary_cat":"math.DG","authors_text":"Paul M. N. Feehan","submitted_at":"2014-09-04T18:47:06Z","abstract_excerpt":"In this monograph, we develop results on global existence and convergence of solutions to abstract gradient flows on Banach spaces for a potential function that obeys the Lojasiewicz-Simon gradient inequality. We prove a Lojasiewicz-Simon gradient inequality for the Yang-Mills energy functional over closed, smooth Riemannian manifolds of arbitrary dimension and apply the resulting framework to prove new results for the gradient flow equation for the Yang-Mills energy functional on a principal bundle, with compact Lie structure group, over a closed, smooth Riemannian manifolds, including the fo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.1525","kind":"arxiv","version":4},"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":"2026-05-18T01:02:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Klcq+QmbvMeQUgeCS9Ou7dv5kV0muh3Odl6uLIxG8oPyIyjj3c/aof2+M/L4Rv7uzQx+uAffnRc7aHgjMf7BCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T14:29:50.551142Z"},"content_sha256":"fdc88464dc9de3e1cfe7720affb9ff8c10b9dc7ae4f30af416251f9172e06fa2","schema_version":"1.0","event_id":"sha256:fdc88464dc9de3e1cfe7720affb9ff8c10b9dc7ae4f30af416251f9172e06fa2"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/O54FTOWAVXCL6XVDXTVDCQKPKW/bundle.json","state_url":"https://pith.science/pith/O54FTOWAVXCL6XVDXTVDCQKPKW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/O54FTOWAVXCL6XVDXTVDCQKPKW/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":"2026-06-03T14:29:50Z","links":{"resolver":"https://pith.science/pith/O54FTOWAVXCL6XVDXTVDCQKPKW","bundle":"https://pith.science/pith/O54FTOWAVXCL6XVDXTVDCQKPKW/bundle.json","state":"https://pith.science/pith/O54FTOWAVXCL6XVDXTVDCQKPKW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/O54FTOWAVXCL6XVDXTVDCQKPKW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:O54FTOWAVXCL6XVDXTVDCQKPKW","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":"d032d74ab4a45a0864189d0d8e5d43e30a30f8fdbc6969ee1b902c55a5d79881","cross_cats_sorted":["math-ph","math.AP","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2014-09-04T18:47:06Z","title_canon_sha256":"2683ccdd0dab9b153837f0de2523b01f8cfbb7151e3c47adf58059fd96309cdf"},"schema_version":"1.0","source":{"id":"1409.1525","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1409.1525","created_at":"2026-05-18T01:02:14Z"},{"alias_kind":"arxiv_version","alias_value":"1409.1525v4","created_at":"2026-05-18T01:02:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1409.1525","created_at":"2026-05-18T01:02:14Z"},{"alias_kind":"pith_short_12","alias_value":"O54FTOWAVXCL","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_16","alias_value":"O54FTOWAVXCL6XVD","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_8","alias_value":"O54FTOWA","created_at":"2026-05-18T12:28:41Z"}],"graph_snapshots":[{"event_id":"sha256:fdc88464dc9de3e1cfe7720affb9ff8c10b9dc7ae4f30af416251f9172e06fa2","target":"graph","created_at":"2026-05-18T01:02:14Z","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":"In this monograph, we develop results on global existence and convergence of solutions to abstract gradient flows on Banach spaces for a potential function that obeys the Lojasiewicz-Simon gradient inequality. We prove a Lojasiewicz-Simon gradient inequality for the Yang-Mills energy functional over closed, smooth Riemannian manifolds of arbitrary dimension and apply the resulting framework to prove new results for the gradient flow equation for the Yang-Mills energy functional on a principal bundle, with compact Lie structure group, over a closed, smooth Riemannian manifolds, including the fo","authors_text":"Paul M. N. Feehan","cross_cats":["math-ph","math.AP","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2014-09-04T18:47:06Z","title":"Global existence and convergence of solutions to gradient systems and applications to Yang-Mills gradient flow"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.1525","kind":"arxiv","version":4},"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:eafa43e39ee386cffc8fc7c6531072eb80a8e751db8cd8a20c8baf309c687910","target":"record","created_at":"2026-05-18T01:02:14Z","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":"d032d74ab4a45a0864189d0d8e5d43e30a30f8fdbc6969ee1b902c55a5d79881","cross_cats_sorted":["math-ph","math.AP","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2014-09-04T18:47:06Z","title_canon_sha256":"2683ccdd0dab9b153837f0de2523b01f8cfbb7151e3c47adf58059fd96309cdf"},"schema_version":"1.0","source":{"id":"1409.1525","kind":"arxiv","version":4}},"canonical_sha256":"777859bac0adc4bf5ea3bcea31414f55bf63b26223959486dd1f5f9e3cc63af6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"777859bac0adc4bf5ea3bcea31414f55bf63b26223959486dd1f5f9e3cc63af6","first_computed_at":"2026-05-18T01:02:14.165797Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:02:14.165797Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"DZJV6XDlgsoM6b30ZtA+0da/2tPi8sVRlPZfeAjsV4pMPQBAtPRPAZWmsczDimHQTz/AMrK4HDFOMU2RLVBuAw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:02:14.166573Z","signed_message":"canonical_sha256_bytes"},"source_id":"1409.1525","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:eafa43e39ee386cffc8fc7c6531072eb80a8e751db8cd8a20c8baf309c687910","sha256:fdc88464dc9de3e1cfe7720affb9ff8c10b9dc7ae4f30af416251f9172e06fa2"],"state_sha256":"08f8a10ad1a3bf5fbd9992d32791c81a6678f12d66a40a45eed97667d23f5060"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lUUryoMABgWeDU+zsdSINhxD1BsBhDSMaZnbK8suT0ytPJo0qeko8FVv2GEl6W9HteYiFLJk1zkF0vGhPsrWCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T14:29:50.553159Z","bundle_sha256":"ba992ca9850f8b0e82a8dc8e95104ed61bfc8a496978710ac2c8925f198dcb56"}}