{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:RD3EJ3A752Z3R6P5NE3YHBHNCO","short_pith_number":"pith:RD3EJ3A7","canonical_record":{"source":{"id":"2606.19433","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2026-06-17T18:00:01Z","cross_cats_sorted":["hep-th","math-ph","math.MP"],"title_canon_sha256":"2a59a3d8acef1bc892614b2295d68b2441711f70390ed15821673b45ceed7ce8","abstract_canon_sha256":"cde3537420c080ee05266a9c8107b3dc69833112cd5973e8ea25629b977aea03"},"schema_version":"1.0"},"canonical_sha256":"88f644ec1feeb3b8f9fd69378384ed13bcf4716edce010a9edb463580b113dd1","source":{"kind":"arxiv","id":"2606.19433","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.19433","created_at":"2026-06-19T16:12:25Z"},{"alias_kind":"arxiv_version","alias_value":"2606.19433v1","created_at":"2026-06-19T16:12:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.19433","created_at":"2026-06-19T16:12:25Z"},{"alias_kind":"pith_short_12","alias_value":"RD3EJ3A752Z3","created_at":"2026-06-19T16:12:25Z"},{"alias_kind":"pith_short_16","alias_value":"RD3EJ3A752Z3R6P5","created_at":"2026-06-19T16:12:25Z"},{"alias_kind":"pith_short_8","alias_value":"RD3EJ3A7","created_at":"2026-06-19T16:12:25Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:RD3EJ3A752Z3R6P5NE3YHBHNCO","target":"record","payload":{"canonical_record":{"source":{"id":"2606.19433","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2026-06-17T18:00:01Z","cross_cats_sorted":["hep-th","math-ph","math.MP"],"title_canon_sha256":"2a59a3d8acef1bc892614b2295d68b2441711f70390ed15821673b45ceed7ce8","abstract_canon_sha256":"cde3537420c080ee05266a9c8107b3dc69833112cd5973e8ea25629b977aea03"},"schema_version":"1.0"},"canonical_sha256":"88f644ec1feeb3b8f9fd69378384ed13bcf4716edce010a9edb463580b113dd1","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-19T16:12:25.553748Z","signature_b64":"yoJ+l026Hwb+FcZSmKU8mTABcGz2RVr9f04FtuW+kRNZyb0giT4aNWQon2GJTr+13DAFG+aPItjHT1Kdd2aeCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"88f644ec1feeb3b8f9fd69378384ed13bcf4716edce010a9edb463580b113dd1","last_reissued_at":"2026-06-19T16:12:25.553383Z","signature_status":"signed_v1","first_computed_at":"2026-06-19T16:12:25.553383Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2606.19433","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":"2026-06-19T16:12:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YEAwA3YTLfWzkD9U2DO5OuJlVpz8GZp2KCGVpNeBUxQobEA90OsPEdKKlhP4H1+AM+Zl8gERsVYMgbxDHYgwCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-28T11:44:16.386416Z"},"content_sha256":"5462fb876dc327bd8c7bab85f7fd4c5f2c058bb416696fd3db28daa0dd2a1ce0","schema_version":"1.0","event_id":"sha256:5462fb876dc327bd8c7bab85f7fd4c5f2c058bb416696fd3db28daa0dd2a1ce0"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:RD3EJ3A752Z3R6P5NE3YHBHNCO","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Exact Solution of the Non-minimally Coupled Klein-Gordon Equation in the Schwarzschild Star","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th","math-ph","math.MP"],"primary_cat":"gr-qc","authors_text":"Kevin T. Grosvenor, Reynan A. Dulinayan","submitted_at":"2026-06-17T18:00:01Z","abstract_excerpt":"We present for the first time the exact solution of the massive Klein-Gordon equation in the Schwarzschild star (perfect-fluid, uniform-density, spherically-symmetric star), including the non-minimal curvature-scalar coupling. The solution is expressed in terms of the general Heun function. A geometry-induced algebraic coordinate transformation reveals a hidden Fuchsian structure that underlies the exact solvability. Known leading- and next-to-leading-order results are recovered in the low-compactness limit. In the Buchdahl limit, we derive a regularity condition for static modes and describe "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.19433","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/2606.19433/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":"2026-06-19T16:12:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XrjUpzRjA3fOet1ei0H8xhGm6GKtcs/GCv/mcPJPhHVw61XpVTAN5RT9WqbADKrnJgKwEQ9BykPBNXVtolweBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-28T11:44:16.386801Z"},"content_sha256":"b27b80c72ae22330d72725860ad5b888c7545ffbeb2ebb7d489e83e25bb7095c","schema_version":"1.0","event_id":"sha256:b27b80c72ae22330d72725860ad5b888c7545ffbeb2ebb7d489e83e25bb7095c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/RD3EJ3A752Z3R6P5NE3YHBHNCO/bundle.json","state_url":"https://pith.science/pith/RD3EJ3A752Z3R6P5NE3YHBHNCO/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/RD3EJ3A752Z3R6P5NE3YHBHNCO/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":"2026-06-28T11:44:16Z","links":{"resolver":"https://pith.science/pith/RD3EJ3A752Z3R6P5NE3YHBHNCO","bundle":"https://pith.science/pith/RD3EJ3A752Z3R6P5NE3YHBHNCO/bundle.json","state":"https://pith.science/pith/RD3EJ3A752Z3R6P5NE3YHBHNCO/state.json","well_known_bundle":"https://pith.science/.well-known/pith/RD3EJ3A752Z3R6P5NE3YHBHNCO/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:RD3EJ3A752Z3R6P5NE3YHBHNCO","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":"cde3537420c080ee05266a9c8107b3dc69833112cd5973e8ea25629b977aea03","cross_cats_sorted":["hep-th","math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2026-06-17T18:00:01Z","title_canon_sha256":"2a59a3d8acef1bc892614b2295d68b2441711f70390ed15821673b45ceed7ce8"},"schema_version":"1.0","source":{"id":"2606.19433","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.19433","created_at":"2026-06-19T16:12:25Z"},{"alias_kind":"arxiv_version","alias_value":"2606.19433v1","created_at":"2026-06-19T16:12:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.19433","created_at":"2026-06-19T16:12:25Z"},{"alias_kind":"pith_short_12","alias_value":"RD3EJ3A752Z3","created_at":"2026-06-19T16:12:25Z"},{"alias_kind":"pith_short_16","alias_value":"RD3EJ3A752Z3R6P5","created_at":"2026-06-19T16:12:25Z"},{"alias_kind":"pith_short_8","alias_value":"RD3EJ3A7","created_at":"2026-06-19T16:12:25Z"}],"graph_snapshots":[{"event_id":"sha256:b27b80c72ae22330d72725860ad5b888c7545ffbeb2ebb7d489e83e25bb7095c","target":"graph","created_at":"2026-06-19T16:12:25Z","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/2606.19433/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We present for the first time the exact solution of the massive Klein-Gordon equation in the Schwarzschild star (perfect-fluid, uniform-density, spherically-symmetric star), including the non-minimal curvature-scalar coupling. The solution is expressed in terms of the general Heun function. A geometry-induced algebraic coordinate transformation reveals a hidden Fuchsian structure that underlies the exact solvability. Known leading- and next-to-leading-order results are recovered in the low-compactness limit. In the Buchdahl limit, we derive a regularity condition for static modes and describe ","authors_text":"Kevin T. Grosvenor, Reynan A. Dulinayan","cross_cats":["hep-th","math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2026-06-17T18:00:01Z","title":"Exact Solution of the Non-minimally Coupled Klein-Gordon Equation in the Schwarzschild Star"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.19433","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":"sha256:5462fb876dc327bd8c7bab85f7fd4c5f2c058bb416696fd3db28daa0dd2a1ce0","target":"record","created_at":"2026-06-19T16:12:25Z","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":"cde3537420c080ee05266a9c8107b3dc69833112cd5973e8ea25629b977aea03","cross_cats_sorted":["hep-th","math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2026-06-17T18:00:01Z","title_canon_sha256":"2a59a3d8acef1bc892614b2295d68b2441711f70390ed15821673b45ceed7ce8"},"schema_version":"1.0","source":{"id":"2606.19433","kind":"arxiv","version":1}},"canonical_sha256":"88f644ec1feeb3b8f9fd69378384ed13bcf4716edce010a9edb463580b113dd1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"88f644ec1feeb3b8f9fd69378384ed13bcf4716edce010a9edb463580b113dd1","first_computed_at":"2026-06-19T16:12:25.553383Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-19T16:12:25.553383Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"yoJ+l026Hwb+FcZSmKU8mTABcGz2RVr9f04FtuW+kRNZyb0giT4aNWQon2GJTr+13DAFG+aPItjHT1Kdd2aeCA==","signature_status":"signed_v1","signed_at":"2026-06-19T16:12:25.553748Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.19433","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5462fb876dc327bd8c7bab85f7fd4c5f2c058bb416696fd3db28daa0dd2a1ce0","sha256:b27b80c72ae22330d72725860ad5b888c7545ffbeb2ebb7d489e83e25bb7095c"],"state_sha256":"1117b3d639e7a355012e5f830d5e8c325cd1e7c2e27f3b27c593c66a9943701d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"A7hPemzdQzTqOi3kCXp9UzuaRlWwbOitmAQDBtf15EaAULsl18k6A0YCt710qoVDdAgPRQZNYkYrGnCuwEzHCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-28T11:44:16.388785Z","bundle_sha256":"a9fbf1dbbe21b3099959297a54abcf124ddc798892779b670fd3da85a064b8ed"}}