{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:1998:54VC7G7OS3U4NXJZ3OCL5GF7YQ","short_pith_number":"pith:54VC7G7O","canonical_record":{"source":{"id":"math/9801073","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.DG","submitted_at":"1998-01-15T12:27:54Z","cross_cats_sorted":["hep-th"],"title_canon_sha256":"4bb0eb1230b4503ae8aeb2f0de4a9fd4920b3747c6d8c5563ae4dee0cc7ff391","abstract_canon_sha256":"c20b4f6bc59e58700a0545ac5c3999fafebe34f7b75a29ad2556bde77396cc73"},"schema_version":"1.0"},"canonical_sha256":"ef2a2f9bee96e9c6dd39db84be98bfc43f0b9930491eb3199c0ce6ecb3fad8d5","source":{"kind":"arxiv","id":"math/9801073","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/9801073","created_at":"2026-05-18T01:05:34Z"},{"alias_kind":"arxiv_version","alias_value":"math/9801073v1","created_at":"2026-05-18T01:05:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/9801073","created_at":"2026-05-18T01:05:34Z"},{"alias_kind":"pith_short_12","alias_value":"54VC7G7OS3U4","created_at":"2026-05-18T12:25:49Z"},{"alias_kind":"pith_short_16","alias_value":"54VC7G7OS3U4NXJZ","created_at":"2026-05-18T12:25:49Z"},{"alias_kind":"pith_short_8","alias_value":"54VC7G7O","created_at":"2026-05-18T12:25:49Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:1998:54VC7G7OS3U4NXJZ3OCL5GF7YQ","target":"record","payload":{"canonical_record":{"source":{"id":"math/9801073","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.DG","submitted_at":"1998-01-15T12:27:54Z","cross_cats_sorted":["hep-th"],"title_canon_sha256":"4bb0eb1230b4503ae8aeb2f0de4a9fd4920b3747c6d8c5563ae4dee0cc7ff391","abstract_canon_sha256":"c20b4f6bc59e58700a0545ac5c3999fafebe34f7b75a29ad2556bde77396cc73"},"schema_version":"1.0"},"canonical_sha256":"ef2a2f9bee96e9c6dd39db84be98bfc43f0b9930491eb3199c0ce6ecb3fad8d5","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:05:34.422925Z","signature_b64":"fxj/pr7+cT7OPPR63GEAuV9E8m+uCZS9r5ulbQvEi3uC7QPWzcynAE5YUxoFSmyB+rDUv/2c4He7JSLyrz60AQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ef2a2f9bee96e9c6dd39db84be98bfc43f0b9930491eb3199c0ce6ecb3fad8d5","last_reissued_at":"2026-05-18T01:05:34.422250Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:05:34.422250Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math/9801073","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":"2026-05-18T01:05:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jIk1xGMflxyWUVvUryH9p2J6Xfmorx3E2CLIqV3IIaBn0OFe5DUeo7VmsSV3G1qhqrAlWTuVjPD9YIhGQgorBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T10:31:33.109466Z"},"content_sha256":"43f34822cf0111a54e57942a0914b24f1107444fab5f461cb5ea2580124696c6","schema_version":"1.0","event_id":"sha256:43f34822cf0111a54e57942a0914b24f1107444fab5f461cb5ea2580124696c6"},{"event_type":"graph_snapshot","subject_pith_number":"pith:1998:54VC7G7OS3U4NXJZ3OCL5GF7YQ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On a Generalisation of the Poincare-Cartan Form to Classical Field Theory","license":"","headline":"","cross_cats":["hep-th"],"primary_cat":"math.DG","authors_text":"Dan Radu Grigore","submitted_at":"1998-01-15T12:27:54Z","abstract_excerpt":"We present here a possible generalisation of the Poincar\\'e-Cartan form in classical field theory in the most general case: arbitrary dimension, arbitrary order of the theory and in the absence of a fibre bundle structure. We use for the kinematical description of the system the $(r,n)$-Grassmann manifold associated to a given manifold $X$, i.e. the manifold of $r$-contact elements of $n$-dimensional submanifolds of $X$. The idea is to define globally a $n+1$ form on this Grassmann manifold, more precisely its class with respect to a certain subspace and to write it locally as the exterior der"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9801073","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":"2026-05-18T01:05:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MUJ3Wt3ecD3Go0wVri5z6vFa8SlXWrIIexXjOEFb7k7qpYMwBfiLJ+RzZ03ycDcinBH/U1ibYfTz9zZUFuskDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T10:31:33.109816Z"},"content_sha256":"4556f868c326cea3d9520499e9b71b49b99ca4da1e4ba04acb5aa69352b5ddd8","schema_version":"1.0","event_id":"sha256:4556f868c326cea3d9520499e9b71b49b99ca4da1e4ba04acb5aa69352b5ddd8"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/54VC7G7OS3U4NXJZ3OCL5GF7YQ/bundle.json","state_url":"https://pith.science/pith/54VC7G7OS3U4NXJZ3OCL5GF7YQ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/54VC7G7OS3U4NXJZ3OCL5GF7YQ/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":"2026-06-11T10:31:33Z","links":{"resolver":"https://pith.science/pith/54VC7G7OS3U4NXJZ3OCL5GF7YQ","bundle":"https://pith.science/pith/54VC7G7OS3U4NXJZ3OCL5GF7YQ/bundle.json","state":"https://pith.science/pith/54VC7G7OS3U4NXJZ3OCL5GF7YQ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/54VC7G7OS3U4NXJZ3OCL5GF7YQ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:1998:54VC7G7OS3U4NXJZ3OCL5GF7YQ","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":"c20b4f6bc59e58700a0545ac5c3999fafebe34f7b75a29ad2556bde77396cc73","cross_cats_sorted":["hep-th"],"license":"","primary_cat":"math.DG","submitted_at":"1998-01-15T12:27:54Z","title_canon_sha256":"4bb0eb1230b4503ae8aeb2f0de4a9fd4920b3747c6d8c5563ae4dee0cc7ff391"},"schema_version":"1.0","source":{"id":"math/9801073","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/9801073","created_at":"2026-05-18T01:05:34Z"},{"alias_kind":"arxiv_version","alias_value":"math/9801073v1","created_at":"2026-05-18T01:05:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/9801073","created_at":"2026-05-18T01:05:34Z"},{"alias_kind":"pith_short_12","alias_value":"54VC7G7OS3U4","created_at":"2026-05-18T12:25:49Z"},{"alias_kind":"pith_short_16","alias_value":"54VC7G7OS3U4NXJZ","created_at":"2026-05-18T12:25:49Z"},{"alias_kind":"pith_short_8","alias_value":"54VC7G7O","created_at":"2026-05-18T12:25:49Z"}],"graph_snapshots":[{"event_id":"sha256:4556f868c326cea3d9520499e9b71b49b99ca4da1e4ba04acb5aa69352b5ddd8","target":"graph","created_at":"2026-05-18T01:05:34Z","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":"We present here a possible generalisation of the Poincar\\'e-Cartan form in classical field theory in the most general case: arbitrary dimension, arbitrary order of the theory and in the absence of a fibre bundle structure. We use for the kinematical description of the system the $(r,n)$-Grassmann manifold associated to a given manifold $X$, i.e. the manifold of $r$-contact elements of $n$-dimensional submanifolds of $X$. The idea is to define globally a $n+1$ form on this Grassmann manifold, more precisely its class with respect to a certain subspace and to write it locally as the exterior der","authors_text":"Dan Radu Grigore","cross_cats":["hep-th"],"headline":"","license":"","primary_cat":"math.DG","submitted_at":"1998-01-15T12:27:54Z","title":"On a Generalisation of the Poincare-Cartan Form to Classical Field Theory"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9801073","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":"sha256:43f34822cf0111a54e57942a0914b24f1107444fab5f461cb5ea2580124696c6","target":"record","created_at":"2026-05-18T01:05:34Z","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":"c20b4f6bc59e58700a0545ac5c3999fafebe34f7b75a29ad2556bde77396cc73","cross_cats_sorted":["hep-th"],"license":"","primary_cat":"math.DG","submitted_at":"1998-01-15T12:27:54Z","title_canon_sha256":"4bb0eb1230b4503ae8aeb2f0de4a9fd4920b3747c6d8c5563ae4dee0cc7ff391"},"schema_version":"1.0","source":{"id":"math/9801073","kind":"arxiv","version":1}},"canonical_sha256":"ef2a2f9bee96e9c6dd39db84be98bfc43f0b9930491eb3199c0ce6ecb3fad8d5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ef2a2f9bee96e9c6dd39db84be98bfc43f0b9930491eb3199c0ce6ecb3fad8d5","first_computed_at":"2026-05-18T01:05:34.422250Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:05:34.422250Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"fxj/pr7+cT7OPPR63GEAuV9E8m+uCZS9r5ulbQvEi3uC7QPWzcynAE5YUxoFSmyB+rDUv/2c4He7JSLyrz60AQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:05:34.422925Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/9801073","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:43f34822cf0111a54e57942a0914b24f1107444fab5f461cb5ea2580124696c6","sha256:4556f868c326cea3d9520499e9b71b49b99ca4da1e4ba04acb5aa69352b5ddd8"],"state_sha256":"005a59c315d5e6952e0b4e304e01ea3bb1493260266f352184e91daccabbb139"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"w94GV1xWmysp/BKdxsfV7JNOZNy9M+Lk2k5lwau4F/A3zi5KjbQuktHKzFi6mnY52RjaVORYBrAbhODMDvUyDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-11T10:31:33.111778Z","bundle_sha256":"b50880400a97f75a8eaeb8fea796859587ac34dc8c50db427a31b71e6816c9dd"}}