{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:HMKKEJ6AT64NTXUBJU5HOMB47F","short_pith_number":"pith:HMKKEJ6A","canonical_record":{"source":{"id":"2505.16101","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math-ph","submitted_at":"2025-05-22T01:02:44Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"6cbb1138a8a2d7eb6e98a7a5cbad22686bff032afe904218e299745e1659c482","abstract_canon_sha256":"f9b203c703bbe27adb1eae3e3e2b6583ff53dd33ac03edfc1a4b6985462cdd1b"},"schema_version":"1.0"},"canonical_sha256":"3b14a227c09fb8d9de814d3a77303cf97e39dc1af5fb70a20e4289162d22760f","source":{"kind":"arxiv","id":"2505.16101","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2505.16101","created_at":"2026-07-05T11:07:29Z"},{"alias_kind":"arxiv_version","alias_value":"2505.16101v1","created_at":"2026-07-05T11:07:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2505.16101","created_at":"2026-07-05T11:07:29Z"},{"alias_kind":"pith_short_12","alias_value":"HMKKEJ6AT64N","created_at":"2026-07-05T11:07:29Z"},{"alias_kind":"pith_short_16","alias_value":"HMKKEJ6AT64NTXUB","created_at":"2026-07-05T11:07:29Z"},{"alias_kind":"pith_short_8","alias_value":"HMKKEJ6A","created_at":"2026-07-05T11:07:29Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:HMKKEJ6AT64NTXUBJU5HOMB47F","target":"record","payload":{"canonical_record":{"source":{"id":"2505.16101","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math-ph","submitted_at":"2025-05-22T01:02:44Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"6cbb1138a8a2d7eb6e98a7a5cbad22686bff032afe904218e299745e1659c482","abstract_canon_sha256":"f9b203c703bbe27adb1eae3e3e2b6583ff53dd33ac03edfc1a4b6985462cdd1b"},"schema_version":"1.0"},"canonical_sha256":"3b14a227c09fb8d9de814d3a77303cf97e39dc1af5fb70a20e4289162d22760f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:07:29.956686Z","signature_b64":"UI6wS4AGKeIoJd7HCIIxbmTJSKgXlzN0I8esa0g/+6de1ThtF8F78Zg8V5MeBxydyWVrtbGiDXl94haoa4rpAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3b14a227c09fb8d9de814d3a77303cf97e39dc1af5fb70a20e4289162d22760f","last_reissued_at":"2026-07-05T11:07:29.956190Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:07:29.956190Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2505.16101","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":"2026-07-05T11:07:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RqTzBncRxaNSSVuM2Q7Ld5yV4QS1wFWVGh8hnA/FvRWywX0sIOmSDXs/dq0m/92qleKd7MjJfZ3Jt1cLZtLtCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-14T19:16:35.797491Z"},"content_sha256":"254f5fc5d900b0cdf52da4ab4efecc14ca6629645b86c7232a9c00d9dc7a4e36","schema_version":"1.0","event_id":"sha256:254f5fc5d900b0cdf52da4ab4efecc14ca6629645b86c7232a9c00d9dc7a4e36"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:HMKKEJ6AT64NTXUBJU5HOMB47F","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Uniqueness of star central configurations in the $5$-body problem","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Leasly A. Campa-Raymundo, Luis Franco-P\\'erez","submitted_at":"2025-05-22T01:02:44Z","abstract_excerpt":"In this study, we present a rigorous analytical proof of the uniqueness of central configurations for the five-body problem, assuming that all five masses are equal and positioned at the vertices of a planar polygon. We consider configurations in which the bodies are equally spaced in angular position relative to the center of mass, and aim to determine whether a central configuration arises under these constraints. We prove that the only central configuration that satisfies these conditions occurs when the five bodies form a regular pentagon. Our approach is entirely analytical, relying on al"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.16101","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/2505.16101/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":"2026-07-05T11:07:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7e1ulK0WOMqNqYyUMdWRFWYswhWavwZwOiO+bTvacMGfsla362U8ayNa/STOJW7Ca81D15LLqHrHuJBXRtN3AA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-14T19:16:35.798065Z"},"content_sha256":"66e3866c5588ecbd96f88bdd0d75b3d14459ca99d409570e92b6fb27e11706fc","schema_version":"1.0","event_id":"sha256:66e3866c5588ecbd96f88bdd0d75b3d14459ca99d409570e92b6fb27e11706fc"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HMKKEJ6AT64NTXUBJU5HOMB47F/bundle.json","state_url":"https://pith.science/pith/HMKKEJ6AT64NTXUBJU5HOMB47F/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HMKKEJ6AT64NTXUBJU5HOMB47F/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":"2026-08-14T19:16:35Z","links":{"resolver":"https://pith.science/pith/HMKKEJ6AT64NTXUBJU5HOMB47F","bundle":"https://pith.science/pith/HMKKEJ6AT64NTXUBJU5HOMB47F/bundle.json","state":"https://pith.science/pith/HMKKEJ6AT64NTXUBJU5HOMB47F/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HMKKEJ6AT64NTXUBJU5HOMB47F/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:HMKKEJ6AT64NTXUBJU5HOMB47F","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":"f9b203c703bbe27adb1eae3e3e2b6583ff53dd33ac03edfc1a4b6985462cdd1b","cross_cats_sorted":["math.MP"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math-ph","submitted_at":"2025-05-22T01:02:44Z","title_canon_sha256":"6cbb1138a8a2d7eb6e98a7a5cbad22686bff032afe904218e299745e1659c482"},"schema_version":"1.0","source":{"id":"2505.16101","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2505.16101","created_at":"2026-07-05T11:07:29Z"},{"alias_kind":"arxiv_version","alias_value":"2505.16101v1","created_at":"2026-07-05T11:07:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2505.16101","created_at":"2026-07-05T11:07:29Z"},{"alias_kind":"pith_short_12","alias_value":"HMKKEJ6AT64N","created_at":"2026-07-05T11:07:29Z"},{"alias_kind":"pith_short_16","alias_value":"HMKKEJ6AT64NTXUB","created_at":"2026-07-05T11:07:29Z"},{"alias_kind":"pith_short_8","alias_value":"HMKKEJ6A","created_at":"2026-07-05T11:07:29Z"}],"graph_snapshots":[{"event_id":"sha256:66e3866c5588ecbd96f88bdd0d75b3d14459ca99d409570e92b6fb27e11706fc","target":"graph","created_at":"2026-07-05T11:07:29Z","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/2505.16101/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this study, we present a rigorous analytical proof of the uniqueness of central configurations for the five-body problem, assuming that all five masses are equal and positioned at the vertices of a planar polygon. We consider configurations in which the bodies are equally spaced in angular position relative to the center of mass, and aim to determine whether a central configuration arises under these constraints. We prove that the only central configuration that satisfies these conditions occurs when the five bodies form a regular pentagon. Our approach is entirely analytical, relying on al","authors_text":"Leasly A. Campa-Raymundo, Luis Franco-P\\'erez","cross_cats":["math.MP"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math-ph","submitted_at":"2025-05-22T01:02:44Z","title":"Uniqueness of star central configurations in the $5$-body problem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.16101","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":"sha256:254f5fc5d900b0cdf52da4ab4efecc14ca6629645b86c7232a9c00d9dc7a4e36","target":"record","created_at":"2026-07-05T11:07:29Z","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":"f9b203c703bbe27adb1eae3e3e2b6583ff53dd33ac03edfc1a4b6985462cdd1b","cross_cats_sorted":["math.MP"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math-ph","submitted_at":"2025-05-22T01:02:44Z","title_canon_sha256":"6cbb1138a8a2d7eb6e98a7a5cbad22686bff032afe904218e299745e1659c482"},"schema_version":"1.0","source":{"id":"2505.16101","kind":"arxiv","version":1}},"canonical_sha256":"3b14a227c09fb8d9de814d3a77303cf97e39dc1af5fb70a20e4289162d22760f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3b14a227c09fb8d9de814d3a77303cf97e39dc1af5fb70a20e4289162d22760f","first_computed_at":"2026-07-05T11:07:29.956190Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:07:29.956190Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"UI6wS4AGKeIoJd7HCIIxbmTJSKgXlzN0I8esa0g/+6de1ThtF8F78Zg8V5MeBxydyWVrtbGiDXl94haoa4rpAg==","signature_status":"signed_v1","signed_at":"2026-07-05T11:07:29.956686Z","signed_message":"canonical_sha256_bytes"},"source_id":"2505.16101","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:254f5fc5d900b0cdf52da4ab4efecc14ca6629645b86c7232a9c00d9dc7a4e36","sha256:66e3866c5588ecbd96f88bdd0d75b3d14459ca99d409570e92b6fb27e11706fc"],"state_sha256":"fdb14d12f198d62096cd3e0c26568ee4d2d35dd041e470ddb2c518c4bbc35e98"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/QRV3KtkPrNhCOCnVztfqpBOaI15H1lFbVDX1+yVs1VBGQiUjksj0NJn/0WtwKtQyCT8MX6rrNl5y3gxf4N4DQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-14T19:16:35.804023Z","bundle_sha256":"867f294db6d9a87777aa33a9d836c0095ab85d1d727829d9a9325ee52579d9dc"}}