{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:1999:FEXTGTSU7TRGADCK2IUC4JJTBI","short_pith_number":"pith:FEXTGTSU","canonical_record":{"source":{"id":"hep-th/9912009","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"hep-th","submitted_at":"1999-12-01T19:00:25Z","cross_cats_sorted":[],"title_canon_sha256":"12480659c541dd4891851fc9348bda7b75ab60348b03cf85584e6e12f16e76d5","abstract_canon_sha256":"4eaeed41b03fe96d36f0a2d2c5c298260bf568903916fed16a3245480a36a28f"},"schema_version":"1.0"},"canonical_sha256":"292f334e54fce2600c4ad2282e25330a09885c9733f0b8c29dbc8e9357aa6e7a","source":{"kind":"arxiv","id":"hep-th/9912009","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"hep-th/9912009","created_at":"2026-07-04T16:15:03Z"},{"alias_kind":"arxiv_version","alias_value":"hep-th/9912009v2","created_at":"2026-07-04T16:15:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.hep-th/9912009","created_at":"2026-07-04T16:15:03Z"},{"alias_kind":"pith_short_12","alias_value":"FEXTGTSU7TRG","created_at":"2026-07-04T16:15:03Z"},{"alias_kind":"pith_short_16","alias_value":"FEXTGTSU7TRGADCK","created_at":"2026-07-04T16:15:03Z"},{"alias_kind":"pith_short_8","alias_value":"FEXTGTSU","created_at":"2026-07-04T16:15:03Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:1999:FEXTGTSU7TRGADCK2IUC4JJTBI","target":"record","payload":{"canonical_record":{"source":{"id":"hep-th/9912009","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"hep-th","submitted_at":"1999-12-01T19:00:25Z","cross_cats_sorted":[],"title_canon_sha256":"12480659c541dd4891851fc9348bda7b75ab60348b03cf85584e6e12f16e76d5","abstract_canon_sha256":"4eaeed41b03fe96d36f0a2d2c5c298260bf568903916fed16a3245480a36a28f"},"schema_version":"1.0"},"canonical_sha256":"292f334e54fce2600c4ad2282e25330a09885c9733f0b8c29dbc8e9357aa6e7a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T16:15:03.608975Z","signature_b64":"aTRgwtJ7+U4cQIpwISOrr10hfCgvpnnyphmhZyQWlGbrWStJoWeXXlJlNkpQAed9p8TMyArBzE0lVJhPBw6oBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"292f334e54fce2600c4ad2282e25330a09885c9733f0b8c29dbc8e9357aa6e7a","last_reissued_at":"2026-07-04T16:15:03.608536Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T16:15:03.608536Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"hep-th/9912009","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":"2026-07-04T16:15:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Nf1lf9Ki2XTwjKDNTzshz2u2dLB9OTm89UhGEopwlsilwboHEqAXiz3AD2sD4oaB6bOQk0djKduSyVWR8mN0BQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-03T16:17:46.286458Z"},"content_sha256":"217e1f8abf479c28d26cde6e2b5a80f7e3cc3035852c80aef0b2d9bab0b2214c","schema_version":"1.0","event_id":"sha256:217e1f8abf479c28d26cde6e2b5a80f7e3cc3035852c80aef0b2d9bab0b2214c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:1999:FEXTGTSU7TRGADCK2IUC4JJTBI","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Extremal Curves in 2+1-Dimensional Yang-Mills Theory","license":"","headline":"","cross_cats":[],"primary_cat":"hep-th","authors_text":"Baruch College, CUNY), Gordon W. Semenoff (University of British Columbia), Peter Orland (Graduate Center","submitted_at":"1999-12-01T19:00:25Z","abstract_excerpt":"We examine the structure of the potential energy of 2+1-dimensional Yang-Mills theory on a torus with gauge group SU(2). We use a standard definition of distance on the space of gauge orbits. A curve of extremal potential energy in orbit space defines connections satisfying a certain partial differential equation. We argue that the energy spectrum is gapped because the extremal curves are of finite length. Though classical gluon waves satisfy our differential equation, they are not extremal curves. We construct examples of extremal curves and find how the length of these curves depends on the "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"hep-th/9912009","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/hep-th/9912009/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":"2026-07-04T16:15:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"a6s4Rh0psoEWL6VUTerM+tt4LANbbo3bPz9TO//dmDoDt1i4zsrOSH8g9/v7oIlZisSKdaY8JuZlLisEXqM8Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-03T16:17:46.286976Z"},"content_sha256":"91fc10709425c4ec14f22c93a605f51b77e358ca3698bfbef1826f51eb323be3","schema_version":"1.0","event_id":"sha256:91fc10709425c4ec14f22c93a605f51b77e358ca3698bfbef1826f51eb323be3"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/FEXTGTSU7TRGADCK2IUC4JJTBI/bundle.json","state_url":"https://pith.science/pith/FEXTGTSU7TRGADCK2IUC4JJTBI/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/FEXTGTSU7TRGADCK2IUC4JJTBI/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":"2026-08-03T16:17:46Z","links":{"resolver":"https://pith.science/pith/FEXTGTSU7TRGADCK2IUC4JJTBI","bundle":"https://pith.science/pith/FEXTGTSU7TRGADCK2IUC4JJTBI/bundle.json","state":"https://pith.science/pith/FEXTGTSU7TRGADCK2IUC4JJTBI/state.json","well_known_bundle":"https://pith.science/.well-known/pith/FEXTGTSU7TRGADCK2IUC4JJTBI/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:1999:FEXTGTSU7TRGADCK2IUC4JJTBI","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":"4eaeed41b03fe96d36f0a2d2c5c298260bf568903916fed16a3245480a36a28f","cross_cats_sorted":[],"license":"","primary_cat":"hep-th","submitted_at":"1999-12-01T19:00:25Z","title_canon_sha256":"12480659c541dd4891851fc9348bda7b75ab60348b03cf85584e6e12f16e76d5"},"schema_version":"1.0","source":{"id":"hep-th/9912009","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"hep-th/9912009","created_at":"2026-07-04T16:15:03Z"},{"alias_kind":"arxiv_version","alias_value":"hep-th/9912009v2","created_at":"2026-07-04T16:15:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.hep-th/9912009","created_at":"2026-07-04T16:15:03Z"},{"alias_kind":"pith_short_12","alias_value":"FEXTGTSU7TRG","created_at":"2026-07-04T16:15:03Z"},{"alias_kind":"pith_short_16","alias_value":"FEXTGTSU7TRGADCK","created_at":"2026-07-04T16:15:03Z"},{"alias_kind":"pith_short_8","alias_value":"FEXTGTSU","created_at":"2026-07-04T16:15:03Z"}],"graph_snapshots":[{"event_id":"sha256:91fc10709425c4ec14f22c93a605f51b77e358ca3698bfbef1826f51eb323be3","target":"graph","created_at":"2026-07-04T16:15:03Z","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/hep-th/9912009/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We examine the structure of the potential energy of 2+1-dimensional Yang-Mills theory on a torus with gauge group SU(2). We use a standard definition of distance on the space of gauge orbits. A curve of extremal potential energy in orbit space defines connections satisfying a certain partial differential equation. We argue that the energy spectrum is gapped because the extremal curves are of finite length. Though classical gluon waves satisfy our differential equation, they are not extremal curves. We construct examples of extremal curves and find how the length of these curves depends on the ","authors_text":"Baruch College, CUNY), Gordon W. Semenoff (University of British Columbia), Peter Orland (Graduate Center","cross_cats":[],"headline":"","license":"","primary_cat":"hep-th","submitted_at":"1999-12-01T19:00:25Z","title":"Extremal Curves in 2+1-Dimensional Yang-Mills Theory"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"hep-th/9912009","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":"sha256:217e1f8abf479c28d26cde6e2b5a80f7e3cc3035852c80aef0b2d9bab0b2214c","target":"record","created_at":"2026-07-04T16:15:03Z","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":"4eaeed41b03fe96d36f0a2d2c5c298260bf568903916fed16a3245480a36a28f","cross_cats_sorted":[],"license":"","primary_cat":"hep-th","submitted_at":"1999-12-01T19:00:25Z","title_canon_sha256":"12480659c541dd4891851fc9348bda7b75ab60348b03cf85584e6e12f16e76d5"},"schema_version":"1.0","source":{"id":"hep-th/9912009","kind":"arxiv","version":2}},"canonical_sha256":"292f334e54fce2600c4ad2282e25330a09885c9733f0b8c29dbc8e9357aa6e7a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"292f334e54fce2600c4ad2282e25330a09885c9733f0b8c29dbc8e9357aa6e7a","first_computed_at":"2026-07-04T16:15:03.608536Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T16:15:03.608536Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"aTRgwtJ7+U4cQIpwISOrr10hfCgvpnnyphmhZyQWlGbrWStJoWeXXlJlNkpQAed9p8TMyArBzE0lVJhPBw6oBQ==","signature_status":"signed_v1","signed_at":"2026-07-04T16:15:03.608975Z","signed_message":"canonical_sha256_bytes"},"source_id":"hep-th/9912009","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:217e1f8abf479c28d26cde6e2b5a80f7e3cc3035852c80aef0b2d9bab0b2214c","sha256:91fc10709425c4ec14f22c93a605f51b77e358ca3698bfbef1826f51eb323be3"],"state_sha256":"aca47a76a5f04ebc1061137cf6cce17b2d470cff6d23f0a0d0444d6a1c115ebe"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7ko0PRITFgpwTTIpR5MCP75oc+455oH/FJOSsna2kZVteLzOM0zws5+BHm2849n/0HFRWxWtcyjha7w+wahKCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-03T16:17:46.290967Z","bundle_sha256":"67a5205f2eb898a4b62ed927bb6c00b043494869720f8ad74539d6a8a8943a34"}}