{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:P3345YOP6VHYDXVD2E73GW63HE","short_pith_number":"pith:P3345YOP","canonical_record":{"source":{"id":"2506.19555","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2025-06-24T12:07:17Z","cross_cats_sorted":[],"title_canon_sha256":"ecd6619176b6071d4b77bb3cf236db70ebd0c5dea2e1b5a87d404224c9904da7","abstract_canon_sha256":"9d7afb42907eeea4a9b5cb8ef9472b0942afaeed6376ca4aa6221cdab420aca7"},"schema_version":"1.0"},"canonical_sha256":"7ef7cee1cff54f81dea3d13fb35bdb3939b131de39d23f0551a3202bef8de91a","source":{"kind":"arxiv","id":"2506.19555","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2506.19555","created_at":"2026-07-05T11:26:34Z"},{"alias_kind":"arxiv_version","alias_value":"2506.19555v1","created_at":"2026-07-05T11:26:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.19555","created_at":"2026-07-05T11:26:34Z"},{"alias_kind":"pith_short_12","alias_value":"P3345YOP6VHY","created_at":"2026-07-05T11:26:34Z"},{"alias_kind":"pith_short_16","alias_value":"P3345YOP6VHYDXVD","created_at":"2026-07-05T11:26:34Z"},{"alias_kind":"pith_short_8","alias_value":"P3345YOP","created_at":"2026-07-05T11:26:34Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:P3345YOP6VHYDXVD2E73GW63HE","target":"record","payload":{"canonical_record":{"source":{"id":"2506.19555","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2025-06-24T12:07:17Z","cross_cats_sorted":[],"title_canon_sha256":"ecd6619176b6071d4b77bb3cf236db70ebd0c5dea2e1b5a87d404224c9904da7","abstract_canon_sha256":"9d7afb42907eeea4a9b5cb8ef9472b0942afaeed6376ca4aa6221cdab420aca7"},"schema_version":"1.0"},"canonical_sha256":"7ef7cee1cff54f81dea3d13fb35bdb3939b131de39d23f0551a3202bef8de91a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:26:34.481710Z","signature_b64":"+ZC8673zRKQA0UeZrv97D3jIHdBySTfrxU36D7d7Sq9wRA96bXNHcg1qhuKbY9Q5Ayh8wHj0haPhIBcUeEpCBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7ef7cee1cff54f81dea3d13fb35bdb3939b131de39d23f0551a3202bef8de91a","last_reissued_at":"2026-07-05T11:26:34.481156Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:26:34.481156Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2506.19555","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":"2026-07-05T11:26:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hYloq0z5jnDgjxvGLlTPphsgreHdGuEKsQ6vFCsdrECIoY+dPhkDcvRXYlMjTlJ17vg92I6Uv7A2qgblisALBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-14T08:10:00.278111Z"},"content_sha256":"7300844b9014f88afac9dee31a8770e441f71ef4a01104eeb388fc154f1b99ad","schema_version":"1.0","event_id":"sha256:7300844b9014f88afac9dee31a8770e441f71ef4a01104eeb388fc154f1b99ad"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:P3345YOP6VHYDXVD2E73GW63HE","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Existence of a constant-mean-curvature hypertorus in \\(S^4\\) via computer assistance","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Oscar Perdomo","submitted_at":"2025-06-24T12:07:17Z","abstract_excerpt":"The round Taylor method uses rational arithmetic, allowing control of both round-off and truncation errors in approximating solutions of differential equations. In this paper, we employ this method together with the Poincare-Miranda theorem to prove the existence of a new embedded constant mean curvature (CMC) hypertorus in the unit four dimensional sphere"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.19555","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/2506.19555/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":"2026-07-05T11:26:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yT++IsD6vpSgM+LxYOaN02AHPXIOBsp1zJwNySTQcZ75zkw2UagH32SMrl3v2/wpChFd+VxuUgZUu20U5vsnDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-14T08:10:00.278993Z"},"content_sha256":"5584b143f762e300076d2192fe50121c2dc0b011d933b5470fa532d2299f22f0","schema_version":"1.0","event_id":"sha256:5584b143f762e300076d2192fe50121c2dc0b011d933b5470fa532d2299f22f0"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/P3345YOP6VHYDXVD2E73GW63HE/bundle.json","state_url":"https://pith.science/pith/P3345YOP6VHYDXVD2E73GW63HE/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/P3345YOP6VHYDXVD2E73GW63HE/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":"2026-08-14T08:10:00Z","links":{"resolver":"https://pith.science/pith/P3345YOP6VHYDXVD2E73GW63HE","bundle":"https://pith.science/pith/P3345YOP6VHYDXVD2E73GW63HE/bundle.json","state":"https://pith.science/pith/P3345YOP6VHYDXVD2E73GW63HE/state.json","well_known_bundle":"https://pith.science/.well-known/pith/P3345YOP6VHYDXVD2E73GW63HE/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:P3345YOP6VHYDXVD2E73GW63HE","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":"9d7afb42907eeea4a9b5cb8ef9472b0942afaeed6376ca4aa6221cdab420aca7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2025-06-24T12:07:17Z","title_canon_sha256":"ecd6619176b6071d4b77bb3cf236db70ebd0c5dea2e1b5a87d404224c9904da7"},"schema_version":"1.0","source":{"id":"2506.19555","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2506.19555","created_at":"2026-07-05T11:26:34Z"},{"alias_kind":"arxiv_version","alias_value":"2506.19555v1","created_at":"2026-07-05T11:26:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.19555","created_at":"2026-07-05T11:26:34Z"},{"alias_kind":"pith_short_12","alias_value":"P3345YOP6VHY","created_at":"2026-07-05T11:26:34Z"},{"alias_kind":"pith_short_16","alias_value":"P3345YOP6VHYDXVD","created_at":"2026-07-05T11:26:34Z"},{"alias_kind":"pith_short_8","alias_value":"P3345YOP","created_at":"2026-07-05T11:26:34Z"}],"graph_snapshots":[{"event_id":"sha256:5584b143f762e300076d2192fe50121c2dc0b011d933b5470fa532d2299f22f0","target":"graph","created_at":"2026-07-05T11:26:34Z","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/2506.19555/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The round Taylor method uses rational arithmetic, allowing control of both round-off and truncation errors in approximating solutions of differential equations. In this paper, we employ this method together with the Poincare-Miranda theorem to prove the existence of a new embedded constant mean curvature (CMC) hypertorus in the unit four dimensional sphere","authors_text":"Oscar Perdomo","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2025-06-24T12:07:17Z","title":"Existence of a constant-mean-curvature hypertorus in \\(S^4\\) via computer assistance"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.19555","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":"sha256:7300844b9014f88afac9dee31a8770e441f71ef4a01104eeb388fc154f1b99ad","target":"record","created_at":"2026-07-05T11:26:34Z","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":"9d7afb42907eeea4a9b5cb8ef9472b0942afaeed6376ca4aa6221cdab420aca7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2025-06-24T12:07:17Z","title_canon_sha256":"ecd6619176b6071d4b77bb3cf236db70ebd0c5dea2e1b5a87d404224c9904da7"},"schema_version":"1.0","source":{"id":"2506.19555","kind":"arxiv","version":1}},"canonical_sha256":"7ef7cee1cff54f81dea3d13fb35bdb3939b131de39d23f0551a3202bef8de91a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7ef7cee1cff54f81dea3d13fb35bdb3939b131de39d23f0551a3202bef8de91a","first_computed_at":"2026-07-05T11:26:34.481156Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:26:34.481156Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+ZC8673zRKQA0UeZrv97D3jIHdBySTfrxU36D7d7Sq9wRA96bXNHcg1qhuKbY9Q5Ayh8wHj0haPhIBcUeEpCBw==","signature_status":"signed_v1","signed_at":"2026-07-05T11:26:34.481710Z","signed_message":"canonical_sha256_bytes"},"source_id":"2506.19555","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7300844b9014f88afac9dee31a8770e441f71ef4a01104eeb388fc154f1b99ad","sha256:5584b143f762e300076d2192fe50121c2dc0b011d933b5470fa532d2299f22f0"],"state_sha256":"c164eae48c3f6380bdfe90c8c91242c59cd4ba02f4b34cd1221cd1a1b4eff856"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1KsWLz6xCzOorArBpd2MgBZery0vB+rE6sQ75t3207TL1ptaxbDwvROBcbLp7/xLf6QG7GkGbYzx9KAjFFEeDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-14T08:10:00.286650Z","bundle_sha256":"5a60c982c13e9939b135d2303caac61ec90e472632133bacf148c94f3040e534"}}