{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2004:4JL5JGOPJULLJW3X3MAPU2LSZ4","short_pith_number":"pith:4JL5JGOP","canonical_record":{"source":{"id":"hep-th/0401093","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"hep-th","submitted_at":"2004-01-13T23:47:08Z","cross_cats_sorted":[],"title_canon_sha256":"0a1c3d97d6680f8a11198f70f67947169eeed19c5b1b500fdfa9b8457f0d4711","abstract_canon_sha256":"21c0f5ecc89dadb7201601e41b83c46ef38fc5c012ccadbc20efe42903d27868"},"schema_version":"1.0"},"canonical_sha256":"e257d499cf4d16b4db77db00fa6972cf25ecc6ccbca27c593563629bba1dce25","source":{"kind":"arxiv","id":"hep-th/0401093","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"hep-th/0401093","created_at":"2026-05-18T04:17:36Z"},{"alias_kind":"arxiv_version","alias_value":"hep-th/0401093v2","created_at":"2026-05-18T04:17:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.hep-th/0401093","created_at":"2026-05-18T04:17:36Z"},{"alias_kind":"pith_short_12","alias_value":"4JL5JGOPJULL","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_16","alias_value":"4JL5JGOPJULLJW3X","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_8","alias_value":"4JL5JGOP","created_at":"2026-05-18T12:25:52Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2004:4JL5JGOPJULLJW3X3MAPU2LSZ4","target":"record","payload":{"canonical_record":{"source":{"id":"hep-th/0401093","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"hep-th","submitted_at":"2004-01-13T23:47:08Z","cross_cats_sorted":[],"title_canon_sha256":"0a1c3d97d6680f8a11198f70f67947169eeed19c5b1b500fdfa9b8457f0d4711","abstract_canon_sha256":"21c0f5ecc89dadb7201601e41b83c46ef38fc5c012ccadbc20efe42903d27868"},"schema_version":"1.0"},"canonical_sha256":"e257d499cf4d16b4db77db00fa6972cf25ecc6ccbca27c593563629bba1dce25","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:17:36.046082Z","signature_b64":"+bjlgSkeZReN4B4YgGChuY6cyB7dyU6d2Com6mFSBBvEm7qExNqYiK59t1joZQYEKbtg6u5WuDgCsq19QV7QAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e257d499cf4d16b4db77db00fa6972cf25ecc6ccbca27c593563629bba1dce25","last_reissued_at":"2026-05-18T04:17:36.045653Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:17:36.045653Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"hep-th/0401093","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":"2026-05-18T04:17:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xknDmU78Vl1kbmsgQPqO6DMG33rlmV9szPdbqhp6tufaQqQJEuICnL4NYmuig5B0XpjzLGr1XKStJ2kz9FwcAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-03T22:10:43.020929Z"},"content_sha256":"470dc8f277aad71a74211506a9005b991941967a911cf0c5579c11bbf08df23e","schema_version":"1.0","event_id":"sha256:470dc8f277aad71a74211506a9005b991941967a911cf0c5579c11bbf08df23e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2004:4JL5JGOPJULLJW3X3MAPU2LSZ4","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Generalizations of Yang-Mills Theory with Nonlinear Constitutive Equations","license":"","headline":"","cross_cats":[],"primary_cat":"hep-th","authors_text":"Gerald A. Goldin, Vladimir Shtelen","submitted_at":"2004-01-13T23:47:08Z","abstract_excerpt":"We generalize classical Yang-Mills theory by extending nonlinear constitutive equations for Maxwell fields to non-Abelian gauge groups. Such theories may or may not be Lagrangian. We obtain conditions on the constitutive equations specifying the Lagrangian case, of which recently-discussed non-Abelian Born-Infeld theories are particular examples. Some models in our class possess nontrivial Galilean (c goes to infinity) limits; we determine when such limits exist, and obtain them explicitly."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"hep-th/0401093","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":""},"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":"2026-05-18T04:17:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4d8ZoctmpALKD5PgDsPcVCK67M9pldGt7sK5Em1m6tDvIQu87XnxSvDOXGKedazlytmvmnepFfMUDZy6himVCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-03T22:10:43.021560Z"},"content_sha256":"1accee20297633a09d123d505ec8fd39e84c88a613635aee4e621c3ce8d3a711","schema_version":"1.0","event_id":"sha256:1accee20297633a09d123d505ec8fd39e84c88a613635aee4e621c3ce8d3a711"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/4JL5JGOPJULLJW3X3MAPU2LSZ4/bundle.json","state_url":"https://pith.science/pith/4JL5JGOPJULLJW3X3MAPU2LSZ4/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/4JL5JGOPJULLJW3X3MAPU2LSZ4/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":"2026-07-03T22:10:43Z","links":{"resolver":"https://pith.science/pith/4JL5JGOPJULLJW3X3MAPU2LSZ4","bundle":"https://pith.science/pith/4JL5JGOPJULLJW3X3MAPU2LSZ4/bundle.json","state":"https://pith.science/pith/4JL5JGOPJULLJW3X3MAPU2LSZ4/state.json","well_known_bundle":"https://pith.science/.well-known/pith/4JL5JGOPJULLJW3X3MAPU2LSZ4/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2004:4JL5JGOPJULLJW3X3MAPU2LSZ4","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":"21c0f5ecc89dadb7201601e41b83c46ef38fc5c012ccadbc20efe42903d27868","cross_cats_sorted":[],"license":"","primary_cat":"hep-th","submitted_at":"2004-01-13T23:47:08Z","title_canon_sha256":"0a1c3d97d6680f8a11198f70f67947169eeed19c5b1b500fdfa9b8457f0d4711"},"schema_version":"1.0","source":{"id":"hep-th/0401093","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"hep-th/0401093","created_at":"2026-05-18T04:17:36Z"},{"alias_kind":"arxiv_version","alias_value":"hep-th/0401093v2","created_at":"2026-05-18T04:17:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.hep-th/0401093","created_at":"2026-05-18T04:17:36Z"},{"alias_kind":"pith_short_12","alias_value":"4JL5JGOPJULL","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_16","alias_value":"4JL5JGOPJULLJW3X","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_8","alias_value":"4JL5JGOP","created_at":"2026-05-18T12:25:52Z"}],"graph_snapshots":[{"event_id":"sha256:1accee20297633a09d123d505ec8fd39e84c88a613635aee4e621c3ce8d3a711","target":"graph","created_at":"2026-05-18T04:17:36Z","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 generalize classical Yang-Mills theory by extending nonlinear constitutive equations for Maxwell fields to non-Abelian gauge groups. Such theories may or may not be Lagrangian. We obtain conditions on the constitutive equations specifying the Lagrangian case, of which recently-discussed non-Abelian Born-Infeld theories are particular examples. Some models in our class possess nontrivial Galilean (c goes to infinity) limits; we determine when such limits exist, and obtain them explicitly.","authors_text":"Gerald A. Goldin, Vladimir Shtelen","cross_cats":[],"headline":"","license":"","primary_cat":"hep-th","submitted_at":"2004-01-13T23:47:08Z","title":"Generalizations of Yang-Mills Theory with Nonlinear Constitutive Equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"hep-th/0401093","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":"sha256:470dc8f277aad71a74211506a9005b991941967a911cf0c5579c11bbf08df23e","target":"record","created_at":"2026-05-18T04:17:36Z","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":"21c0f5ecc89dadb7201601e41b83c46ef38fc5c012ccadbc20efe42903d27868","cross_cats_sorted":[],"license":"","primary_cat":"hep-th","submitted_at":"2004-01-13T23:47:08Z","title_canon_sha256":"0a1c3d97d6680f8a11198f70f67947169eeed19c5b1b500fdfa9b8457f0d4711"},"schema_version":"1.0","source":{"id":"hep-th/0401093","kind":"arxiv","version":2}},"canonical_sha256":"e257d499cf4d16b4db77db00fa6972cf25ecc6ccbca27c593563629bba1dce25","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e257d499cf4d16b4db77db00fa6972cf25ecc6ccbca27c593563629bba1dce25","first_computed_at":"2026-05-18T04:17:36.045653Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:17:36.045653Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+bjlgSkeZReN4B4YgGChuY6cyB7dyU6d2Com6mFSBBvEm7qExNqYiK59t1joZQYEKbtg6u5WuDgCsq19QV7QAg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:17:36.046082Z","signed_message":"canonical_sha256_bytes"},"source_id":"hep-th/0401093","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:470dc8f277aad71a74211506a9005b991941967a911cf0c5579c11bbf08df23e","sha256:1accee20297633a09d123d505ec8fd39e84c88a613635aee4e621c3ce8d3a711"],"state_sha256":"78539a26ac9e0391df7a9406f986c03467141789f6191ce45ac133355a9ef407"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LyUjhXVclUAbd2c/GeFuWWx8DClu+XbyirMvcO4CE6HubLjpJY8vf6qyiVQ1qCp8Kt8Lo98qynLcu6SfmpW8Aw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-03T22:10:43.024384Z","bundle_sha256":"78e1f42f484515d72493b644e9cff727d77529d428293ce3949c44d766dde3e3"}}