{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:1997:GMQ6JZFN527YUY4UZS3FOZNJ3K","short_pith_number":"pith:GMQ6JZFN","canonical_record":{"source":{"id":"gr-qc/9701046","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"gr-qc","submitted_at":"1997-01-21T03:42:02Z","cross_cats_sorted":[],"title_canon_sha256":"d544767f4822a11af55a995168129b3595e9b3bdf20b32e10c97555e681b3b59","abstract_canon_sha256":"683408811a52862222a588e7cce00addd2d3b8d62bb6915b33d3f7ad0f8e3570"},"schema_version":"1.0"},"canonical_sha256":"3321e4e4adeebf8a6394ccb65765a9daa72b701ad8ebdec64f379598c71503a2","source":{"kind":"arxiv","id":"gr-qc/9701046","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"gr-qc/9701046","created_at":"2026-05-18T01:39:19Z"},{"alias_kind":"arxiv_version","alias_value":"gr-qc/9701046v1","created_at":"2026-05-18T01:39:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.gr-qc/9701046","created_at":"2026-05-18T01:39:19Z"},{"alias_kind":"pith_short_12","alias_value":"GMQ6JZFN527Y","created_at":"2026-05-18T12:25:48Z"},{"alias_kind":"pith_short_16","alias_value":"GMQ6JZFN527YUY4U","created_at":"2026-05-18T12:25:48Z"},{"alias_kind":"pith_short_8","alias_value":"GMQ6JZFN","created_at":"2026-05-18T12:25:48Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:1997:GMQ6JZFN527YUY4UZS3FOZNJ3K","target":"record","payload":{"canonical_record":{"source":{"id":"gr-qc/9701046","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"gr-qc","submitted_at":"1997-01-21T03:42:02Z","cross_cats_sorted":[],"title_canon_sha256":"d544767f4822a11af55a995168129b3595e9b3bdf20b32e10c97555e681b3b59","abstract_canon_sha256":"683408811a52862222a588e7cce00addd2d3b8d62bb6915b33d3f7ad0f8e3570"},"schema_version":"1.0"},"canonical_sha256":"3321e4e4adeebf8a6394ccb65765a9daa72b701ad8ebdec64f379598c71503a2","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:39:19.143625Z","signature_b64":"sCHaKIueICGRpVISDf6ybLz7M2oHLcOaivvXcZGavyX/7d+ki+xBvmm1p5vJgJipet2zviup/MujLu9GcmQiBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3321e4e4adeebf8a6394ccb65765a9daa72b701ad8ebdec64f379598c71503a2","last_reissued_at":"2026-05-18T01:39:19.142786Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:39:19.142786Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"gr-qc/9701046","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":"2026-05-18T01:39:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IukQEKIjzZ8Nq0uzQo51qn8xQncbVwR8UwaIo4e4oZDnFFGkUiyIFUYgZdwRFh8TZ2AR7arC7OkD8rrHHF1rAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T17:26:01.580909Z"},"content_sha256":"b0b545b6dbb5c571ba9920d9e22cc745c55e777f903492ad30a34b11a8c20905","schema_version":"1.0","event_id":"sha256:b0b545b6dbb5c571ba9920d9e22cc745c55e777f903492ad30a34b11a8c20905"},{"event_type":"graph_snapshot","subject_pith_number":"pith:1997:GMQ6JZFN527YUY4UZS3FOZNJ3K","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Tensor distributions on signature-changing space-times","license":"","headline":"","cross_cats":[],"primary_cat":"gr-qc","authors_text":"David Hartley, Philip A. Tuckey, Robin W. Tucker, Tevian Dray","submitted_at":"1997-01-21T03:42:02Z","abstract_excerpt":"Irregularities in the metric tensor of a signature-changing space-time suggest that field equations on such space-times might be regarded as distributional. We review the formalism of tensor distributions on differentiable manifolds, and examine to what extent rigorous meaning can be given to field equations in the presence of signature-change, in particular those involving covariant derivatives. We find that, for both continuous and discontinuous signature-change, covariant differentiation can be defined on a class of tensor distributions wide enough to be physically interesting."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"gr-qc/9701046","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":"2026-05-18T01:39:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wddObBoMvXpY0urvbl27cYWW/iyHMKBI9/AOtT9Idw6FP+osORKzlI5wqyEboZ+rEVi5gV7Vd0/dl2W1qnxhBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T17:26:01.581253Z"},"content_sha256":"e55bc3c06ac0014d5fcb15551958fcb54e6c74c8b0e54ec6c747c2380193d0a4","schema_version":"1.0","event_id":"sha256:e55bc3c06ac0014d5fcb15551958fcb54e6c74c8b0e54ec6c747c2380193d0a4"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GMQ6JZFN527YUY4UZS3FOZNJ3K/bundle.json","state_url":"https://pith.science/pith/GMQ6JZFN527YUY4UZS3FOZNJ3K/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GMQ6JZFN527YUY4UZS3FOZNJ3K/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":"2026-06-21T17:26:01Z","links":{"resolver":"https://pith.science/pith/GMQ6JZFN527YUY4UZS3FOZNJ3K","bundle":"https://pith.science/pith/GMQ6JZFN527YUY4UZS3FOZNJ3K/bundle.json","state":"https://pith.science/pith/GMQ6JZFN527YUY4UZS3FOZNJ3K/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GMQ6JZFN527YUY4UZS3FOZNJ3K/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:1997:GMQ6JZFN527YUY4UZS3FOZNJ3K","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":"683408811a52862222a588e7cce00addd2d3b8d62bb6915b33d3f7ad0f8e3570","cross_cats_sorted":[],"license":"","primary_cat":"gr-qc","submitted_at":"1997-01-21T03:42:02Z","title_canon_sha256":"d544767f4822a11af55a995168129b3595e9b3bdf20b32e10c97555e681b3b59"},"schema_version":"1.0","source":{"id":"gr-qc/9701046","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"gr-qc/9701046","created_at":"2026-05-18T01:39:19Z"},{"alias_kind":"arxiv_version","alias_value":"gr-qc/9701046v1","created_at":"2026-05-18T01:39:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.gr-qc/9701046","created_at":"2026-05-18T01:39:19Z"},{"alias_kind":"pith_short_12","alias_value":"GMQ6JZFN527Y","created_at":"2026-05-18T12:25:48Z"},{"alias_kind":"pith_short_16","alias_value":"GMQ6JZFN527YUY4U","created_at":"2026-05-18T12:25:48Z"},{"alias_kind":"pith_short_8","alias_value":"GMQ6JZFN","created_at":"2026-05-18T12:25:48Z"}],"graph_snapshots":[{"event_id":"sha256:e55bc3c06ac0014d5fcb15551958fcb54e6c74c8b0e54ec6c747c2380193d0a4","target":"graph","created_at":"2026-05-18T01:39:19Z","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":"Irregularities in the metric tensor of a signature-changing space-time suggest that field equations on such space-times might be regarded as distributional. We review the formalism of tensor distributions on differentiable manifolds, and examine to what extent rigorous meaning can be given to field equations in the presence of signature-change, in particular those involving covariant derivatives. We find that, for both continuous and discontinuous signature-change, covariant differentiation can be defined on a class of tensor distributions wide enough to be physically interesting.","authors_text":"David Hartley, Philip A. Tuckey, Robin W. Tucker, Tevian Dray","cross_cats":[],"headline":"","license":"","primary_cat":"gr-qc","submitted_at":"1997-01-21T03:42:02Z","title":"Tensor distributions on signature-changing space-times"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"gr-qc/9701046","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:b0b545b6dbb5c571ba9920d9e22cc745c55e777f903492ad30a34b11a8c20905","target":"record","created_at":"2026-05-18T01:39:19Z","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":"683408811a52862222a588e7cce00addd2d3b8d62bb6915b33d3f7ad0f8e3570","cross_cats_sorted":[],"license":"","primary_cat":"gr-qc","submitted_at":"1997-01-21T03:42:02Z","title_canon_sha256":"d544767f4822a11af55a995168129b3595e9b3bdf20b32e10c97555e681b3b59"},"schema_version":"1.0","source":{"id":"gr-qc/9701046","kind":"arxiv","version":1}},"canonical_sha256":"3321e4e4adeebf8a6394ccb65765a9daa72b701ad8ebdec64f379598c71503a2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3321e4e4adeebf8a6394ccb65765a9daa72b701ad8ebdec64f379598c71503a2","first_computed_at":"2026-05-18T01:39:19.142786Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:39:19.142786Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"sCHaKIueICGRpVISDf6ybLz7M2oHLcOaivvXcZGavyX/7d+ki+xBvmm1p5vJgJipet2zviup/MujLu9GcmQiBA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:39:19.143625Z","signed_message":"canonical_sha256_bytes"},"source_id":"gr-qc/9701046","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b0b545b6dbb5c571ba9920d9e22cc745c55e777f903492ad30a34b11a8c20905","sha256:e55bc3c06ac0014d5fcb15551958fcb54e6c74c8b0e54ec6c747c2380193d0a4"],"state_sha256":"9c7cb387af9eb37706f74167b558ecaeaf6dc78c61d15beb8285db4589bcbdcf"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tADaJwMJP7rizxs2ysEwXqSW/7Nd4UvMmseaKo3Fjv6tSVvUxQT4R0+Q0JOr3h2PCQpKhWk6yM3YE6bky++GBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-21T17:26:01.583399Z","bundle_sha256":"1182f43f7c98801fb681ce080a00a0536eb655de73aa2c239fb232c38e5770e0"}}