{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2001:DWXZ7WC72EUDHD7YG5OSQM6YNM","short_pith_number":"pith:DWXZ7WC7","canonical_record":{"source":{"id":"math-ph/0112033","kind":"arxiv","version":3},"metadata":{"license":"","primary_cat":"math-ph","submitted_at":"2001-12-17T11:40:03Z","cross_cats_sorted":["hep-th","math.MP"],"title_canon_sha256":"d56e7d9655410f8b22f6ed07505cae7ff3ef6555681dcd021999023cef7ae9c2","abstract_canon_sha256":"7aaa523fb13352a0357fa717c27c25735431b5ba84f9cc717a652677e2b0bbba"},"schema_version":"1.0"},"canonical_sha256":"1daf9fd85fd128338ff8375d2833d86b05fd63fe6bc706234d96f30a90e13bd3","source":{"kind":"arxiv","id":"math-ph/0112033","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math-ph/0112033","created_at":"2026-05-18T01:38:34Z"},{"alias_kind":"arxiv_version","alias_value":"math-ph/0112033v3","created_at":"2026-05-18T01:38:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math-ph/0112033","created_at":"2026-05-18T01:38:34Z"},{"alias_kind":"pith_short_12","alias_value":"DWXZ7WC72EUD","created_at":"2026-05-18T12:25:50Z"},{"alias_kind":"pith_short_16","alias_value":"DWXZ7WC72EUDHD7Y","created_at":"2026-05-18T12:25:50Z"},{"alias_kind":"pith_short_8","alias_value":"DWXZ7WC7","created_at":"2026-05-18T12:25:50Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2001:DWXZ7WC72EUDHD7YG5OSQM6YNM","target":"record","payload":{"canonical_record":{"source":{"id":"math-ph/0112033","kind":"arxiv","version":3},"metadata":{"license":"","primary_cat":"math-ph","submitted_at":"2001-12-17T11:40:03Z","cross_cats_sorted":["hep-th","math.MP"],"title_canon_sha256":"d56e7d9655410f8b22f6ed07505cae7ff3ef6555681dcd021999023cef7ae9c2","abstract_canon_sha256":"7aaa523fb13352a0357fa717c27c25735431b5ba84f9cc717a652677e2b0bbba"},"schema_version":"1.0"},"canonical_sha256":"1daf9fd85fd128338ff8375d2833d86b05fd63fe6bc706234d96f30a90e13bd3","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:38:34.370581Z","signature_b64":"1KXnmia7T7aUcUuM8l6nkmK9c2EuDyy2WDwXEgPtngVzMFB85mSC1W8Mz25qQy5xxKp/jd6v+gZ2h/Sl5IiiCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1daf9fd85fd128338ff8375d2833d86b05fd63fe6bc706234d96f30a90e13bd3","last_reissued_at":"2026-05-18T01:38:34.370034Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:38:34.370034Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math-ph/0112033","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":"2026-05-18T01:38:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uH+9Dd/zk97DVxaX5a5pQDMN1bSUS/xBTm/wyicgS2xMQVtesRvtEuYzQXW1J1shFGugdOf21Uvhk4eLKKFSCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T05:31:07.689119Z"},"content_sha256":"6e5f165741a3d83cc677e27018a640d897372ae67036e84abf322d5508c69330","schema_version":"1.0","event_id":"sha256:6e5f165741a3d83cc677e27018a640d897372ae67036e84abf322d5508c69330"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2001:DWXZ7WC72EUDHD7YG5OSQM6YNM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A universal solution","license":"","headline":"","cross_cats":["hep-th","math.MP"],"primary_cat":"math-ph","authors_text":"D. B. Fairlie","submitted_at":"2001-12-17T11:40:03Z","abstract_excerpt":"The phenomenon of an implicit function which solves a large set of second order partial differential equations obtainable from a variational principle is explicated by the introduction of a class of universal solutions to the equations derivable from an arbitrary Lagrangian which is homogeneous of weight one in the field derivatives. This result is extended to many fields. The imposition of Lorentz invariance makes such Lagrangians unique, and equivalent to the Companion Lagrangians introduced in [baker]."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math-ph/0112033","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":"2026-05-18T01:38:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"auke6APboREKzII0f4iwU5o+6qirwU70xSXaSSTzRBqO9N2y4B9CORKVvJLfb9y4UBKhAgV3fkbZq7Lx4BgECg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T05:31:07.689485Z"},"content_sha256":"fdaf6f25e9da2d48090ffd3a030245c10627febe29d36b0ca28ade3ba23fcdea","schema_version":"1.0","event_id":"sha256:fdaf6f25e9da2d48090ffd3a030245c10627febe29d36b0ca28ade3ba23fcdea"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/DWXZ7WC72EUDHD7YG5OSQM6YNM/bundle.json","state_url":"https://pith.science/pith/DWXZ7WC72EUDHD7YG5OSQM6YNM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/DWXZ7WC72EUDHD7YG5OSQM6YNM/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":"2026-06-25T05:31:07Z","links":{"resolver":"https://pith.science/pith/DWXZ7WC72EUDHD7YG5OSQM6YNM","bundle":"https://pith.science/pith/DWXZ7WC72EUDHD7YG5OSQM6YNM/bundle.json","state":"https://pith.science/pith/DWXZ7WC72EUDHD7YG5OSQM6YNM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/DWXZ7WC72EUDHD7YG5OSQM6YNM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2001:DWXZ7WC72EUDHD7YG5OSQM6YNM","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":"7aaa523fb13352a0357fa717c27c25735431b5ba84f9cc717a652677e2b0bbba","cross_cats_sorted":["hep-th","math.MP"],"license":"","primary_cat":"math-ph","submitted_at":"2001-12-17T11:40:03Z","title_canon_sha256":"d56e7d9655410f8b22f6ed07505cae7ff3ef6555681dcd021999023cef7ae9c2"},"schema_version":"1.0","source":{"id":"math-ph/0112033","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math-ph/0112033","created_at":"2026-05-18T01:38:34Z"},{"alias_kind":"arxiv_version","alias_value":"math-ph/0112033v3","created_at":"2026-05-18T01:38:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math-ph/0112033","created_at":"2026-05-18T01:38:34Z"},{"alias_kind":"pith_short_12","alias_value":"DWXZ7WC72EUD","created_at":"2026-05-18T12:25:50Z"},{"alias_kind":"pith_short_16","alias_value":"DWXZ7WC72EUDHD7Y","created_at":"2026-05-18T12:25:50Z"},{"alias_kind":"pith_short_8","alias_value":"DWXZ7WC7","created_at":"2026-05-18T12:25:50Z"}],"graph_snapshots":[{"event_id":"sha256:fdaf6f25e9da2d48090ffd3a030245c10627febe29d36b0ca28ade3ba23fcdea","target":"graph","created_at":"2026-05-18T01:38:34Z","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":"The phenomenon of an implicit function which solves a large set of second order partial differential equations obtainable from a variational principle is explicated by the introduction of a class of universal solutions to the equations derivable from an arbitrary Lagrangian which is homogeneous of weight one in the field derivatives. This result is extended to many fields. The imposition of Lorentz invariance makes such Lagrangians unique, and equivalent to the Companion Lagrangians introduced in [baker].","authors_text":"D. B. Fairlie","cross_cats":["hep-th","math.MP"],"headline":"","license":"","primary_cat":"math-ph","submitted_at":"2001-12-17T11:40:03Z","title":"A universal solution"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math-ph/0112033","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":"sha256:6e5f165741a3d83cc677e27018a640d897372ae67036e84abf322d5508c69330","target":"record","created_at":"2026-05-18T01:38:34Z","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":"7aaa523fb13352a0357fa717c27c25735431b5ba84f9cc717a652677e2b0bbba","cross_cats_sorted":["hep-th","math.MP"],"license":"","primary_cat":"math-ph","submitted_at":"2001-12-17T11:40:03Z","title_canon_sha256":"d56e7d9655410f8b22f6ed07505cae7ff3ef6555681dcd021999023cef7ae9c2"},"schema_version":"1.0","source":{"id":"math-ph/0112033","kind":"arxiv","version":3}},"canonical_sha256":"1daf9fd85fd128338ff8375d2833d86b05fd63fe6bc706234d96f30a90e13bd3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1daf9fd85fd128338ff8375d2833d86b05fd63fe6bc706234d96f30a90e13bd3","first_computed_at":"2026-05-18T01:38:34.370034Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:38:34.370034Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"1KXnmia7T7aUcUuM8l6nkmK9c2EuDyy2WDwXEgPtngVzMFB85mSC1W8Mz25qQy5xxKp/jd6v+gZ2h/Sl5IiiCA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:38:34.370581Z","signed_message":"canonical_sha256_bytes"},"source_id":"math-ph/0112033","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6e5f165741a3d83cc677e27018a640d897372ae67036e84abf322d5508c69330","sha256:fdaf6f25e9da2d48090ffd3a030245c10627febe29d36b0ca28ade3ba23fcdea"],"state_sha256":"925349d39c5155ca5b4ab5a8dd8d175068e5648196ee611868068e4275b4444f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"P8/Faq+BFFTRFWBpl4cKr0GnoY77wi4MUlr5p/TY74RM1ysCV2zdOxzTIs2wmy1O8BsMf2l0+StM0iTlZ576Bw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-25T05:31:07.691417Z","bundle_sha256":"00bd8cdcc1942d267bc330dc07d4299d3db68e19855f850853cb1f17a13f77d4"}}