{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:VHK3WSHPG5SDSN5CB5KGKBC6TG","short_pith_number":"pith:VHK3WSHP","canonical_record":{"source":{"id":"2411.15264","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"gr-qc","submitted_at":"2024-11-22T10:54:50Z","cross_cats_sorted":[],"title_canon_sha256":"edbbde28dc4ce0a1671088f42f96fb17b6f4281f96717212ca02b363be88ac97","abstract_canon_sha256":"75d39cf392595be261edf2f30cf87526c3e44c3eeb52f18d95215f3dd941345a"},"schema_version":"1.0"},"canonical_sha256":"a9d5bb48ef37643937a20f5465045e9989ef2a02e9276f8ff207a0257d059102","source":{"kind":"arxiv","id":"2411.15264","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2411.15264","created_at":"2026-07-05T09:39:32Z"},{"alias_kind":"arxiv_version","alias_value":"2411.15264v1","created_at":"2026-07-05T09:39:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2411.15264","created_at":"2026-07-05T09:39:32Z"},{"alias_kind":"pith_short_12","alias_value":"VHK3WSHPG5SD","created_at":"2026-07-05T09:39:32Z"},{"alias_kind":"pith_short_16","alias_value":"VHK3WSHPG5SDSN5C","created_at":"2026-07-05T09:39:32Z"},{"alias_kind":"pith_short_8","alias_value":"VHK3WSHP","created_at":"2026-07-05T09:39:32Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:VHK3WSHPG5SDSN5CB5KGKBC6TG","target":"record","payload":{"canonical_record":{"source":{"id":"2411.15264","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"gr-qc","submitted_at":"2024-11-22T10:54:50Z","cross_cats_sorted":[],"title_canon_sha256":"edbbde28dc4ce0a1671088f42f96fb17b6f4281f96717212ca02b363be88ac97","abstract_canon_sha256":"75d39cf392595be261edf2f30cf87526c3e44c3eeb52f18d95215f3dd941345a"},"schema_version":"1.0"},"canonical_sha256":"a9d5bb48ef37643937a20f5465045e9989ef2a02e9276f8ff207a0257d059102","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:39:32.061901Z","signature_b64":"dVKbd0wVvPywW747Ml1w2AMcWJnUl/BGMUByDzBBFdlJJkgNwjWXTF35mF7jcxaMhDQ+uUXeikytWnp2SPY5Bg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a9d5bb48ef37643937a20f5465045e9989ef2a02e9276f8ff207a0257d059102","last_reissued_at":"2026-07-05T09:39:32.061483Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:39:32.061483Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2411.15264","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":"2026-07-05T09:39:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Zd6poNnN++kZWwgOdBc57Kt/8ny6DaflsqR2u7SGxrwC9CpK8eCOXY7DJuz6k8gOeubNGF6R5P8I1PWjBe7aAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-13T11:08:53.300114Z"},"content_sha256":"4b12b2551bcabefd982abfe8934b5fa032253a2c53d55665a18c0f69ae8e58d3","schema_version":"1.0","event_id":"sha256:4b12b2551bcabefd982abfe8934b5fa032253a2c53d55665a18c0f69ae8e58d3"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:VHK3WSHPG5SDSN5CB5KGKBC6TG","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Zero Values of the TOV Equation","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"gr-qc","authors_text":"Jonas Pleyer","submitted_at":"2024-11-22T10:54:50Z","abstract_excerpt":"This thesis calculates the special-relativistic internal energy of a non-interacting gas. We derive an equation of state (EoS) which we apply to the Tollmann-Oppenheimer Volkoff (TOV) equation. Furthermore we present numerical results of the TOV equation for various configurations of a polytropic EoS. These results show that the zero values of the TOV equation compared to its non-relativistic counterpart, the Lane-Emden (LE) equation, are smaller for identical parameters. We present initial developments to a proof of this theorem. Furthermore, an additional exact solution and index $n=2$ of th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.15264","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/2411.15264/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":"2026-07-05T09:39:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kcQwAeeTXZANbqx8An3FxKCbfaWSl6TI+neCQC3XMv2TM7HFv/LkJCB/GLxcg8cKVRs6532K/vv8+7RxPW4EDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-13T11:08:53.301042Z"},"content_sha256":"addc6229a224ba3c8052a63f5a4239dd50a9f13af2a11426be662875ca6d69d0","schema_version":"1.0","event_id":"sha256:addc6229a224ba3c8052a63f5a4239dd50a9f13af2a11426be662875ca6d69d0"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VHK3WSHPG5SDSN5CB5KGKBC6TG/bundle.json","state_url":"https://pith.science/pith/VHK3WSHPG5SDSN5CB5KGKBC6TG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VHK3WSHPG5SDSN5CB5KGKBC6TG/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":"2026-08-13T11:08:53Z","links":{"resolver":"https://pith.science/pith/VHK3WSHPG5SDSN5CB5KGKBC6TG","bundle":"https://pith.science/pith/VHK3WSHPG5SDSN5CB5KGKBC6TG/bundle.json","state":"https://pith.science/pith/VHK3WSHPG5SDSN5CB5KGKBC6TG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VHK3WSHPG5SDSN5CB5KGKBC6TG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:VHK3WSHPG5SDSN5CB5KGKBC6TG","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":"75d39cf392595be261edf2f30cf87526c3e44c3eeb52f18d95215f3dd941345a","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"gr-qc","submitted_at":"2024-11-22T10:54:50Z","title_canon_sha256":"edbbde28dc4ce0a1671088f42f96fb17b6f4281f96717212ca02b363be88ac97"},"schema_version":"1.0","source":{"id":"2411.15264","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2411.15264","created_at":"2026-07-05T09:39:32Z"},{"alias_kind":"arxiv_version","alias_value":"2411.15264v1","created_at":"2026-07-05T09:39:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2411.15264","created_at":"2026-07-05T09:39:32Z"},{"alias_kind":"pith_short_12","alias_value":"VHK3WSHPG5SD","created_at":"2026-07-05T09:39:32Z"},{"alias_kind":"pith_short_16","alias_value":"VHK3WSHPG5SDSN5C","created_at":"2026-07-05T09:39:32Z"},{"alias_kind":"pith_short_8","alias_value":"VHK3WSHP","created_at":"2026-07-05T09:39:32Z"}],"graph_snapshots":[{"event_id":"sha256:addc6229a224ba3c8052a63f5a4239dd50a9f13af2a11426be662875ca6d69d0","target":"graph","created_at":"2026-07-05T09:39:32Z","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/2411.15264/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"This thesis calculates the special-relativistic internal energy of a non-interacting gas. We derive an equation of state (EoS) which we apply to the Tollmann-Oppenheimer Volkoff (TOV) equation. Furthermore we present numerical results of the TOV equation for various configurations of a polytropic EoS. These results show that the zero values of the TOV equation compared to its non-relativistic counterpart, the Lane-Emden (LE) equation, are smaller for identical parameters. We present initial developments to a proof of this theorem. Furthermore, an additional exact solution and index $n=2$ of th","authors_text":"Jonas Pleyer","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"gr-qc","submitted_at":"2024-11-22T10:54:50Z","title":"Zero Values of the TOV Equation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.15264","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":"sha256:4b12b2551bcabefd982abfe8934b5fa032253a2c53d55665a18c0f69ae8e58d3","target":"record","created_at":"2026-07-05T09:39:32Z","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":"75d39cf392595be261edf2f30cf87526c3e44c3eeb52f18d95215f3dd941345a","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"gr-qc","submitted_at":"2024-11-22T10:54:50Z","title_canon_sha256":"edbbde28dc4ce0a1671088f42f96fb17b6f4281f96717212ca02b363be88ac97"},"schema_version":"1.0","source":{"id":"2411.15264","kind":"arxiv","version":1}},"canonical_sha256":"a9d5bb48ef37643937a20f5465045e9989ef2a02e9276f8ff207a0257d059102","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a9d5bb48ef37643937a20f5465045e9989ef2a02e9276f8ff207a0257d059102","first_computed_at":"2026-07-05T09:39:32.061483Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:39:32.061483Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"dVKbd0wVvPywW747Ml1w2AMcWJnUl/BGMUByDzBBFdlJJkgNwjWXTF35mF7jcxaMhDQ+uUXeikytWnp2SPY5Bg==","signature_status":"signed_v1","signed_at":"2026-07-05T09:39:32.061901Z","signed_message":"canonical_sha256_bytes"},"source_id":"2411.15264","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4b12b2551bcabefd982abfe8934b5fa032253a2c53d55665a18c0f69ae8e58d3","sha256:addc6229a224ba3c8052a63f5a4239dd50a9f13af2a11426be662875ca6d69d0"],"state_sha256":"5c84b71dd1bac88834b56ac5fb3a4a1396ba2ebb3b92579e2e79340f1353363f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JZIOBqDtnT33SgmjmLs+TFSy6/fXdjcAvaWg2aEvADw8AduQqHSSuhGweXcrhNoCcuLHgRW9SJnLbWib6KcDBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-13T11:08:53.361467Z","bundle_sha256":"ed41c1bc83bdede645e4fa3a07a341bcef08d847a40e4375c2d7f9f9a2b86c7c"}}