{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:54PGLHLEQFRD3YIOXVNVZLRZAU","short_pith_number":"pith:54PGLHLE","canonical_record":{"source":{"id":"2608.07909","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"gr-qc","submitted_at":"2026-08-08T04:28:15Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"034935ae16fea6b33bdb907bf48c1f8184b5fc85d6d418a8cb166b5088213c89","abstract_canon_sha256":"4f874e16a23b17f16ac228ef8ab2bd5415e766073da8820b5f1a6f2def1e9939"},"schema_version":"1.0"},"canonical_sha256":"ef1e659d6481623de10ebd5b5cae39053b2d17455dfac479db485acfc4a76366","source":{"kind":"arxiv","id":"2608.07909","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2608.07909","created_at":"2026-08-11T01:18:54Z"},{"alias_kind":"arxiv_version","alias_value":"2608.07909v1","created_at":"2026-08-11T01:18:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2608.07909","created_at":"2026-08-11T01:18:54Z"},{"alias_kind":"pith_short_12","alias_value":"54PGLHLEQFRD","created_at":"2026-08-11T01:18:54Z"},{"alias_kind":"pith_short_16","alias_value":"54PGLHLEQFRD3YIO","created_at":"2026-08-11T01:18:54Z"},{"alias_kind":"pith_short_8","alias_value":"54PGLHLE","created_at":"2026-08-11T01:18:54Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:54PGLHLEQFRD3YIOXVNVZLRZAU","target":"record","payload":{"canonical_record":{"source":{"id":"2608.07909","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"gr-qc","submitted_at":"2026-08-08T04:28:15Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"034935ae16fea6b33bdb907bf48c1f8184b5fc85d6d418a8cb166b5088213c89","abstract_canon_sha256":"4f874e16a23b17f16ac228ef8ab2bd5415e766073da8820b5f1a6f2def1e9939"},"schema_version":"1.0"},"canonical_sha256":"ef1e659d6481623de10ebd5b5cae39053b2d17455dfac479db485acfc4a76366","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-08-11T01:18:54.243841Z","signature_b64":"XoDE/WdgHQHQd6d3Q8cnEkh3SbKMAz7MPSodSYzXpbGF4aqFb5KI39rOdyky7570zLlUjECWnEanTtIKIDU8Dg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ef1e659d6481623de10ebd5b5cae39053b2d17455dfac479db485acfc4a76366","last_reissued_at":"2026-08-11T01:18:54.241367Z","signature_status":"signed_v1","first_computed_at":"2026-08-11T01:18:54.241367Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2608.07909","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":"2026-08-11T01:18:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dsvHlJXhxphigudmtNZWopuhUpSjnrnbcAEwPEdUaAYvowJNO3/HUjOPthCeJp7tD8li5YzSd6TvEplybgm5BQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-12T10:21:07.928480Z"},"content_sha256":"78c2ae568139dbc01892b86c8b90f2296b3b029848002ccc457840598def8b74","schema_version":"1.0","event_id":"sha256:78c2ae568139dbc01892b86c8b90f2296b3b029848002ccc457840598def8b74"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:54PGLHLEQFRD3YIOXVNVZLRZAU","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Mapping Schwarzschild Spacetime: From Kruskal to Diamond and Golden Representations","license":"http://creativecommons.org/licenses/by-sa/4.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"gr-qc","authors_text":"Edgar Alejandro Le\\'on","submitted_at":"2026-08-08T04:28:15Z","abstract_excerpt":"We present several representations of the Schwarzschild spacetime. Some of these are classical, such as the embedding, Tortoise, and Kruskal representations. The latter two motivate the introduction of pulsating coordinates (or the Diamond representation), a compact approach recently proposed for spherically symmetric static metrics. We then introduce the Golden representation for the Schwarzschild spacetime, where what we call the Fibonacci metric, and the golden ratio, become ubiquitous. We conclude by offering some visual and physical interpretations of this approach."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.07909","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2608.07909/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-08-11T01:18:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"i/3ZnA6kofOmIcfbJjG3alx7vyZKt1w4blreLYwUq6genX46VXJERPtKdYhLUnxIIMlnxomaDuHlm7y+OLVqCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-12T10:21:07.928996Z"},"content_sha256":"15d0eea839ea77f87d9db0cc5b4590ceee7e83a9aca5c7eafd0c0eeead06ae35","schema_version":"1.0","event_id":"sha256:15d0eea839ea77f87d9db0cc5b4590ceee7e83a9aca5c7eafd0c0eeead06ae35"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/54PGLHLEQFRD3YIOXVNVZLRZAU/bundle.json","state_url":"https://pith.science/pith/54PGLHLEQFRD3YIOXVNVZLRZAU/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/54PGLHLEQFRD3YIOXVNVZLRZAU/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":"2026-08-12T10:21:07Z","links":{"resolver":"https://pith.science/pith/54PGLHLEQFRD3YIOXVNVZLRZAU","bundle":"https://pith.science/pith/54PGLHLEQFRD3YIOXVNVZLRZAU/bundle.json","state":"https://pith.science/pith/54PGLHLEQFRD3YIOXVNVZLRZAU/state.json","well_known_bundle":"https://pith.science/.well-known/pith/54PGLHLEQFRD3YIOXVNVZLRZAU/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:54PGLHLEQFRD3YIOXVNVZLRZAU","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":"4f874e16a23b17f16ac228ef8ab2bd5415e766073da8820b5f1a6f2def1e9939","cross_cats_sorted":["math-ph","math.MP"],"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"gr-qc","submitted_at":"2026-08-08T04:28:15Z","title_canon_sha256":"034935ae16fea6b33bdb907bf48c1f8184b5fc85d6d418a8cb166b5088213c89"},"schema_version":"1.0","source":{"id":"2608.07909","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2608.07909","created_at":"2026-08-11T01:18:54Z"},{"alias_kind":"arxiv_version","alias_value":"2608.07909v1","created_at":"2026-08-11T01:18:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2608.07909","created_at":"2026-08-11T01:18:54Z"},{"alias_kind":"pith_short_12","alias_value":"54PGLHLEQFRD","created_at":"2026-08-11T01:18:54Z"},{"alias_kind":"pith_short_16","alias_value":"54PGLHLEQFRD3YIO","created_at":"2026-08-11T01:18:54Z"},{"alias_kind":"pith_short_8","alias_value":"54PGLHLE","created_at":"2026-08-11T01:18:54Z"}],"graph_snapshots":[{"event_id":"sha256:15d0eea839ea77f87d9db0cc5b4590ceee7e83a9aca5c7eafd0c0eeead06ae35","target":"graph","created_at":"2026-08-11T01:18:54Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2608.07909/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We present several representations of the Schwarzschild spacetime. Some of these are classical, such as the embedding, Tortoise, and Kruskal representations. The latter two motivate the introduction of pulsating coordinates (or the Diamond representation), a compact approach recently proposed for spherically symmetric static metrics. We then introduce the Golden representation for the Schwarzschild spacetime, where what we call the Fibonacci metric, and the golden ratio, become ubiquitous. We conclude by offering some visual and physical interpretations of this approach.","authors_text":"Edgar Alejandro Le\\'on","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"gr-qc","submitted_at":"2026-08-08T04:28:15Z","title":"Mapping Schwarzschild Spacetime: From Kruskal to Diamond and Golden Representations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.07909","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":"sha256:78c2ae568139dbc01892b86c8b90f2296b3b029848002ccc457840598def8b74","target":"record","created_at":"2026-08-11T01:18:54Z","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":"4f874e16a23b17f16ac228ef8ab2bd5415e766073da8820b5f1a6f2def1e9939","cross_cats_sorted":["math-ph","math.MP"],"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"gr-qc","submitted_at":"2026-08-08T04:28:15Z","title_canon_sha256":"034935ae16fea6b33bdb907bf48c1f8184b5fc85d6d418a8cb166b5088213c89"},"schema_version":"1.0","source":{"id":"2608.07909","kind":"arxiv","version":1}},"canonical_sha256":"ef1e659d6481623de10ebd5b5cae39053b2d17455dfac479db485acfc4a76366","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ef1e659d6481623de10ebd5b5cae39053b2d17455dfac479db485acfc4a76366","first_computed_at":"2026-08-11T01:18:54.241367Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-08-11T01:18:54.241367Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"XoDE/WdgHQHQd6d3Q8cnEkh3SbKMAz7MPSodSYzXpbGF4aqFb5KI39rOdyky7570zLlUjECWnEanTtIKIDU8Dg==","signature_status":"signed_v1","signed_at":"2026-08-11T01:18:54.243841Z","signed_message":"canonical_sha256_bytes"},"source_id":"2608.07909","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:78c2ae568139dbc01892b86c8b90f2296b3b029848002ccc457840598def8b74","sha256:15d0eea839ea77f87d9db0cc5b4590ceee7e83a9aca5c7eafd0c0eeead06ae35"],"state_sha256":"cd8377838b0ef9b14ee5f7f78ab160c18cf74d70a443268e2242ff87d894cd76"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Mf6g3wehtjDWG4gYEUzegtyxly/gTO1taqBEBwX7HKxs7OXslrPP96x21fCpkW5UqQ8fsk+uUL8KkJ0WTU8lAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-12T10:21:07.932866Z","bundle_sha256":"89e41b6dd33c76f64ad350383356bcd8d5cfb480bd06b44045f92bfa754ff562"}}