{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2001:P7L3QYTU5S72ZGRRJCEQPHVHGL","short_pith_number":"pith:P7L3QYTU","canonical_record":{"source":{"id":"math-ph/0107027","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math-ph","submitted_at":"2001-07-27T12:55:40Z","cross_cats_sorted":["hep-th","math.MP"],"title_canon_sha256":"b87ab94e1fd5ffe1d503ac04fd4beb795e00cbe9a37da11547f28aee657bc053","abstract_canon_sha256":"94debf5b916bc7167b1e84c20f9667f521460056260bd50f587ec16d9d171a4f"},"schema_version":"1.0"},"canonical_sha256":"7fd7b86274ecbfac9a314889079ea732c8fa405e2ae8805a1694329fc39929c9","source":{"kind":"arxiv","id":"math-ph/0107027","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math-ph/0107027","created_at":"2026-05-18T01:05:32Z"},{"alias_kind":"arxiv_version","alias_value":"math-ph/0107027v1","created_at":"2026-05-18T01:05:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math-ph/0107027","created_at":"2026-05-18T01:05:32Z"},{"alias_kind":"pith_short_12","alias_value":"P7L3QYTU5S72","created_at":"2026-05-18T12:25:50Z"},{"alias_kind":"pith_short_16","alias_value":"P7L3QYTU5S72ZGRR","created_at":"2026-05-18T12:25:50Z"},{"alias_kind":"pith_short_8","alias_value":"P7L3QYTU","created_at":"2026-05-18T12:25:50Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2001:P7L3QYTU5S72ZGRRJCEQPHVHGL","target":"record","payload":{"canonical_record":{"source":{"id":"math-ph/0107027","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math-ph","submitted_at":"2001-07-27T12:55:40Z","cross_cats_sorted":["hep-th","math.MP"],"title_canon_sha256":"b87ab94e1fd5ffe1d503ac04fd4beb795e00cbe9a37da11547f28aee657bc053","abstract_canon_sha256":"94debf5b916bc7167b1e84c20f9667f521460056260bd50f587ec16d9d171a4f"},"schema_version":"1.0"},"canonical_sha256":"7fd7b86274ecbfac9a314889079ea732c8fa405e2ae8805a1694329fc39929c9","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:05:32.065677Z","signature_b64":"e67K9L8O61HT7sITQdT8JiD6BEqzjA/OwfKHAvh5EDtOJQmiQymxYNdWbxf++byJtH+Im8qMNxZWvBxslvT/Dg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7fd7b86274ecbfac9a314889079ea732c8fa405e2ae8805a1694329fc39929c9","last_reissued_at":"2026-05-18T01:05:32.065073Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:05:32.065073Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math-ph/0107027","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":"2026-05-18T01:05:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"iFYcPcmtA7EuE12w9xOOID5I3kaGwP/mK8KxhOEZQWGqWU6t6jMUzt+E/eNlnZ//n+UTWmJ1I0QF0PAZr5xbCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T10:15:11.810201Z"},"content_sha256":"f8ce78c918b169c8d7e1bbc55a2ab2ded58c139a075845ca1b8c9e60c3ccfa25","schema_version":"1.0","event_id":"sha256:f8ce78c918b169c8d7e1bbc55a2ab2ded58c139a075845ca1b8c9e60c3ccfa25"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2001:P7L3QYTU5S72ZGRRJCEQPHVHGL","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Yang-Mills fields as optical media","license":"","headline":"","cross_cats":["hep-th","math.MP"],"primary_cat":"math-ph","authors_text":"A. L. Barbosa, R. Aldrovandi","submitted_at":"2001-07-27T12:55:40Z","abstract_excerpt":"A geometrization of the Yang-Mills field, by which an SU(2) gauge theory becomes equivalent to a 3-space geometry - or optical system - is examined. In a first step, ambient space remains Euclidean and current problems on flat space can be looked at from a new point of view. The Wu-Yang ambiguity, for example, appears related to the multiple possible torsions of distinct metric-preserving connections. In a second step, also the ambient space becomes curved. In general, the strictly Riemannian, metric sector plays the role of an arbitrary host space, with the gauge field represented by a contor"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math-ph/0107027","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":"2026-05-18T01:05:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xqOLiiYFWzMSW5L3GexvvnHqmwMB/A+f9KpJPYhLyS0IItCfW59ruqTp++SD17rmuz76OkYKC9dMUpqVPTtwDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T10:15:11.810870Z"},"content_sha256":"e0f310cccc9e617a213033fb4312dc73158493ed82eb6d6cf36bba14eb9f0eab","schema_version":"1.0","event_id":"sha256:e0f310cccc9e617a213033fb4312dc73158493ed82eb6d6cf36bba14eb9f0eab"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/P7L3QYTU5S72ZGRRJCEQPHVHGL/bundle.json","state_url":"https://pith.science/pith/P7L3QYTU5S72ZGRRJCEQPHVHGL/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/P7L3QYTU5S72ZGRRJCEQPHVHGL/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":"2026-05-30T10:15:11Z","links":{"resolver":"https://pith.science/pith/P7L3QYTU5S72ZGRRJCEQPHVHGL","bundle":"https://pith.science/pith/P7L3QYTU5S72ZGRRJCEQPHVHGL/bundle.json","state":"https://pith.science/pith/P7L3QYTU5S72ZGRRJCEQPHVHGL/state.json","well_known_bundle":"https://pith.science/.well-known/pith/P7L3QYTU5S72ZGRRJCEQPHVHGL/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2001:P7L3QYTU5S72ZGRRJCEQPHVHGL","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":"94debf5b916bc7167b1e84c20f9667f521460056260bd50f587ec16d9d171a4f","cross_cats_sorted":["hep-th","math.MP"],"license":"","primary_cat":"math-ph","submitted_at":"2001-07-27T12:55:40Z","title_canon_sha256":"b87ab94e1fd5ffe1d503ac04fd4beb795e00cbe9a37da11547f28aee657bc053"},"schema_version":"1.0","source":{"id":"math-ph/0107027","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math-ph/0107027","created_at":"2026-05-18T01:05:32Z"},{"alias_kind":"arxiv_version","alias_value":"math-ph/0107027v1","created_at":"2026-05-18T01:05:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math-ph/0107027","created_at":"2026-05-18T01:05:32Z"},{"alias_kind":"pith_short_12","alias_value":"P7L3QYTU5S72","created_at":"2026-05-18T12:25:50Z"},{"alias_kind":"pith_short_16","alias_value":"P7L3QYTU5S72ZGRR","created_at":"2026-05-18T12:25:50Z"},{"alias_kind":"pith_short_8","alias_value":"P7L3QYTU","created_at":"2026-05-18T12:25:50Z"}],"graph_snapshots":[{"event_id":"sha256:e0f310cccc9e617a213033fb4312dc73158493ed82eb6d6cf36bba14eb9f0eab","target":"graph","created_at":"2026-05-18T01:05:32Z","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":"A geometrization of the Yang-Mills field, by which an SU(2) gauge theory becomes equivalent to a 3-space geometry - or optical system - is examined. In a first step, ambient space remains Euclidean and current problems on flat space can be looked at from a new point of view. The Wu-Yang ambiguity, for example, appears related to the multiple possible torsions of distinct metric-preserving connections. In a second step, also the ambient space becomes curved. In general, the strictly Riemannian, metric sector plays the role of an arbitrary host space, with the gauge field represented by a contor","authors_text":"A. L. Barbosa, R. Aldrovandi","cross_cats":["hep-th","math.MP"],"headline":"","license":"","primary_cat":"math-ph","submitted_at":"2001-07-27T12:55:40Z","title":"Yang-Mills fields as optical media"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math-ph/0107027","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:f8ce78c918b169c8d7e1bbc55a2ab2ded58c139a075845ca1b8c9e60c3ccfa25","target":"record","created_at":"2026-05-18T01:05:32Z","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":"94debf5b916bc7167b1e84c20f9667f521460056260bd50f587ec16d9d171a4f","cross_cats_sorted":["hep-th","math.MP"],"license":"","primary_cat":"math-ph","submitted_at":"2001-07-27T12:55:40Z","title_canon_sha256":"b87ab94e1fd5ffe1d503ac04fd4beb795e00cbe9a37da11547f28aee657bc053"},"schema_version":"1.0","source":{"id":"math-ph/0107027","kind":"arxiv","version":1}},"canonical_sha256":"7fd7b86274ecbfac9a314889079ea732c8fa405e2ae8805a1694329fc39929c9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7fd7b86274ecbfac9a314889079ea732c8fa405e2ae8805a1694329fc39929c9","first_computed_at":"2026-05-18T01:05:32.065073Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:05:32.065073Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"e67K9L8O61HT7sITQdT8JiD6BEqzjA/OwfKHAvh5EDtOJQmiQymxYNdWbxf++byJtH+Im8qMNxZWvBxslvT/Dg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:05:32.065677Z","signed_message":"canonical_sha256_bytes"},"source_id":"math-ph/0107027","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f8ce78c918b169c8d7e1bbc55a2ab2ded58c139a075845ca1b8c9e60c3ccfa25","sha256:e0f310cccc9e617a213033fb4312dc73158493ed82eb6d6cf36bba14eb9f0eab"],"state_sha256":"934f88d0d7b0f80c578d24276476651a0c5f9e8bdea31f00ac271a45b79b6f34"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qP+O+mYJiY6G4RnGpEt4K32P47hEih3yW5rgJ2w94sbC5OUFmaYuMhKuL5lJeWdO4MgY27Fymq+EFIOB8zJ6BQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T10:15:11.814003Z","bundle_sha256":"cfd1ee01ddca0544050216809dc89cb8a9b7ae5906bb57432a5a68b2cd55a3f9"}}