{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2009:APDNSJJ7BUDJ5XZSILTG56RO23","short_pith_number":"pith:APDNSJJ7","canonical_record":{"source":{"id":"0907.0454","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2009-07-02T17:57:04Z","cross_cats_sorted":[],"title_canon_sha256":"c5f929cc28858b90ff70440c9654738bb7c600cb136ebde43ab1f8321646759e","abstract_canon_sha256":"430a29c6da29a7b0314e3def5123421eb6c58b9c83e4b6e662678ef3c8d630ba"},"schema_version":"1.0"},"canonical_sha256":"03c6d9253f0d069edf3242e66efa2ed6ee3628089919f29aad1a4689f9f1619f","source":{"kind":"arxiv","id":"0907.0454","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0907.0454","created_at":"2026-05-18T01:17:10Z"},{"alias_kind":"arxiv_version","alias_value":"0907.0454v3","created_at":"2026-05-18T01:17:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0907.0454","created_at":"2026-05-18T01:17:10Z"},{"alias_kind":"pith_short_12","alias_value":"APDNSJJ7BUDJ","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_16","alias_value":"APDNSJJ7BUDJ5XZS","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_8","alias_value":"APDNSJJ7","created_at":"2026-05-18T12:25:58Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2009:APDNSJJ7BUDJ5XZSILTG56RO23","target":"record","payload":{"canonical_record":{"source":{"id":"0907.0454","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2009-07-02T17:57:04Z","cross_cats_sorted":[],"title_canon_sha256":"c5f929cc28858b90ff70440c9654738bb7c600cb136ebde43ab1f8321646759e","abstract_canon_sha256":"430a29c6da29a7b0314e3def5123421eb6c58b9c83e4b6e662678ef3c8d630ba"},"schema_version":"1.0"},"canonical_sha256":"03c6d9253f0d069edf3242e66efa2ed6ee3628089919f29aad1a4689f9f1619f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:17:10.612344Z","signature_b64":"lVuZLDadO73xfjM2u/I3UDXI+ruCxNvclmwy3RHsU6f1kVJul6KVrin5DiOAM9IQ7ERXSGHUc6aozx12/GbeCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"03c6d9253f0d069edf3242e66efa2ed6ee3628089919f29aad1a4689f9f1619f","last_reissued_at":"2026-05-18T01:17:10.611651Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:17:10.611651Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0907.0454","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":"2026-05-18T01:17:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pdxdKQCrYiXYNR787Anx1RoQoJziqHC6R1aYux5h42oiLQXm5gMBpaOkEtlJxJOt8u7TeR7b3NfED1R4y55ZCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T20:56:28.187930Z"},"content_sha256":"8f06d9c0efee9f8cf815ddc3e565780bd44c2f773ee4c8d4b4d0b05373d0e51e","schema_version":"1.0","event_id":"sha256:8f06d9c0efee9f8cf815ddc3e565780bd44c2f773ee4c8d4b4d0b05373d0e51e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2009:APDNSJJ7BUDJ5XZSILTG56RO23","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A survey of group actions on 4-manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Allan L. Edmonds","submitted_at":"2009-07-02T17:57:04Z","abstract_excerpt":"Over 50 years of work on group actions on $4$-manifolds, from the 1960's to the present, from knotted fixed point sets to Seiberg-Witten invariants, is surveyed. Locally linear actions are emphasized, but differentiable and purely topological actions are also discussed. The presentation is organized around some of the fundamental general questions that have driven the subject of compact transformation groups over the years and their interpretations in the case of $4$-manifolds. Many open problems are formulated. Updates to previous problems sets are given. A substantial bibliography is include"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0907.0454","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":"2026-05-18T01:17:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"smAbskX1NWUrQpb+Yt17wyLBt3IIWo5y8RnQV3MljAlMsA4s6U6tksyL5MnIcGOmpZCWD1lSyf7qbtj3it39BQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T20:56:28.188274Z"},"content_sha256":"58a1fecbdf17491c7722cbfa6279ed0bf0dac8608d24fce3d4078b9fb4df3e07","schema_version":"1.0","event_id":"sha256:58a1fecbdf17491c7722cbfa6279ed0bf0dac8608d24fce3d4078b9fb4df3e07"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/APDNSJJ7BUDJ5XZSILTG56RO23/bundle.json","state_url":"https://pith.science/pith/APDNSJJ7BUDJ5XZSILTG56RO23/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/APDNSJJ7BUDJ5XZSILTG56RO23/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":"2026-06-22T20:56:28Z","links":{"resolver":"https://pith.science/pith/APDNSJJ7BUDJ5XZSILTG56RO23","bundle":"https://pith.science/pith/APDNSJJ7BUDJ5XZSILTG56RO23/bundle.json","state":"https://pith.science/pith/APDNSJJ7BUDJ5XZSILTG56RO23/state.json","well_known_bundle":"https://pith.science/.well-known/pith/APDNSJJ7BUDJ5XZSILTG56RO23/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:APDNSJJ7BUDJ5XZSILTG56RO23","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":"430a29c6da29a7b0314e3def5123421eb6c58b9c83e4b6e662678ef3c8d630ba","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2009-07-02T17:57:04Z","title_canon_sha256":"c5f929cc28858b90ff70440c9654738bb7c600cb136ebde43ab1f8321646759e"},"schema_version":"1.0","source":{"id":"0907.0454","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0907.0454","created_at":"2026-05-18T01:17:10Z"},{"alias_kind":"arxiv_version","alias_value":"0907.0454v3","created_at":"2026-05-18T01:17:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0907.0454","created_at":"2026-05-18T01:17:10Z"},{"alias_kind":"pith_short_12","alias_value":"APDNSJJ7BUDJ","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_16","alias_value":"APDNSJJ7BUDJ5XZS","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_8","alias_value":"APDNSJJ7","created_at":"2026-05-18T12:25:58Z"}],"graph_snapshots":[{"event_id":"sha256:58a1fecbdf17491c7722cbfa6279ed0bf0dac8608d24fce3d4078b9fb4df3e07","target":"graph","created_at":"2026-05-18T01:17:10Z","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":"Over 50 years of work on group actions on $4$-manifolds, from the 1960's to the present, from knotted fixed point sets to Seiberg-Witten invariants, is surveyed. Locally linear actions are emphasized, but differentiable and purely topological actions are also discussed. The presentation is organized around some of the fundamental general questions that have driven the subject of compact transformation groups over the years and their interpretations in the case of $4$-manifolds. Many open problems are formulated. Updates to previous problems sets are given. A substantial bibliography is include","authors_text":"Allan L. Edmonds","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2009-07-02T17:57:04Z","title":"A survey of group actions on 4-manifolds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0907.0454","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":"sha256:8f06d9c0efee9f8cf815ddc3e565780bd44c2f773ee4c8d4b4d0b05373d0e51e","target":"record","created_at":"2026-05-18T01:17:10Z","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":"430a29c6da29a7b0314e3def5123421eb6c58b9c83e4b6e662678ef3c8d630ba","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2009-07-02T17:57:04Z","title_canon_sha256":"c5f929cc28858b90ff70440c9654738bb7c600cb136ebde43ab1f8321646759e"},"schema_version":"1.0","source":{"id":"0907.0454","kind":"arxiv","version":3}},"canonical_sha256":"03c6d9253f0d069edf3242e66efa2ed6ee3628089919f29aad1a4689f9f1619f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"03c6d9253f0d069edf3242e66efa2ed6ee3628089919f29aad1a4689f9f1619f","first_computed_at":"2026-05-18T01:17:10.611651Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:17:10.611651Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"lVuZLDadO73xfjM2u/I3UDXI+ruCxNvclmwy3RHsU6f1kVJul6KVrin5DiOAM9IQ7ERXSGHUc6aozx12/GbeCg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:17:10.612344Z","signed_message":"canonical_sha256_bytes"},"source_id":"0907.0454","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8f06d9c0efee9f8cf815ddc3e565780bd44c2f773ee4c8d4b4d0b05373d0e51e","sha256:58a1fecbdf17491c7722cbfa6279ed0bf0dac8608d24fce3d4078b9fb4df3e07"],"state_sha256":"7ce8c1acacf566fac8424eb2efd828ecda661df440381d95447161ebac02d13b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QpSL+bdS8ZIcVeZUHTmw68mrgacLJER41ZoAE0wjeTA1B8+MiXLKxtIfryVWZbPOK9ZKgQzEFfm5TDD0LhGfCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-22T20:56:28.190194Z","bundle_sha256":"2d5a133ad3d3a9376fd1ad6b0b562d888b5f7499eddf49883e78745081a68146"}}