{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:5S5Z4X7JE5DNVLO2HUV74HHITW","short_pith_number":"pith:5S5Z4X7J","canonical_record":{"source":{"id":"2607.00102","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"physics.chem-ph","submitted_at":"2026-06-30T19:42:12Z","cross_cats_sorted":["quant-ph"],"title_canon_sha256":"086fe6251482aaaa6ca9b08ee869391a90f70fe6fb7756a00b30671aeda6a388","abstract_canon_sha256":"2fa2226414e4191002a5c806dfc3fad87bac8e84bdf52006c336b20403e634ee"},"schema_version":"1.0"},"canonical_sha256":"ecbb9e5fe92746daadda3d2bfe1ce89d9de1411bfa342494f1f06e2d2b5f1d52","source":{"kind":"arxiv","id":"2607.00102","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.00102","created_at":"2026-07-02T00:18:34Z"},{"alias_kind":"arxiv_version","alias_value":"2607.00102v1","created_at":"2026-07-02T00:18:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.00102","created_at":"2026-07-02T00:18:34Z"},{"alias_kind":"pith_short_12","alias_value":"5S5Z4X7JE5DN","created_at":"2026-07-02T00:18:34Z"},{"alias_kind":"pith_short_16","alias_value":"5S5Z4X7JE5DNVLO2","created_at":"2026-07-02T00:18:34Z"},{"alias_kind":"pith_short_8","alias_value":"5S5Z4X7J","created_at":"2026-07-02T00:18:34Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:5S5Z4X7JE5DNVLO2HUV74HHITW","target":"record","payload":{"canonical_record":{"source":{"id":"2607.00102","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"physics.chem-ph","submitted_at":"2026-06-30T19:42:12Z","cross_cats_sorted":["quant-ph"],"title_canon_sha256":"086fe6251482aaaa6ca9b08ee869391a90f70fe6fb7756a00b30671aeda6a388","abstract_canon_sha256":"2fa2226414e4191002a5c806dfc3fad87bac8e84bdf52006c336b20403e634ee"},"schema_version":"1.0"},"canonical_sha256":"ecbb9e5fe92746daadda3d2bfe1ce89d9de1411bfa342494f1f06e2d2b5f1d52","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-02T00:18:34.519967Z","signature_b64":"Dz7OFqWcsCWotF/vYXAoX5C1to679Bj7beYOxfxJWqoHz3KulsTjbv9Bw833kHH8pJ3S4JPQjf4WGOb5prfxBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ecbb9e5fe92746daadda3d2bfe1ce89d9de1411bfa342494f1f06e2d2b5f1d52","last_reissued_at":"2026-07-02T00:18:34.519441Z","signature_status":"signed_v1","first_computed_at":"2026-07-02T00:18:34.519441Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2607.00102","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":"2026-07-02T00:18:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ES53Q8bQ7Er3TO64CJPyNGJnfhe9teDQy9kSqd+HnG153HT+eU89IfV5uDk/ihr4gq26iQin5DBuJ8Ta/ToXDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-03T08:16:52.373574Z"},"content_sha256":"4c96eaed05f545e12882ca37ca116df94d6d223bf2fdab448948536c38505b61","schema_version":"1.0","event_id":"sha256:4c96eaed05f545e12882ca37ca116df94d6d223bf2fdab448948536c38505b61"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:5S5Z4X7JE5DNVLO2HUV74HHITW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A differential derivation of the Obara-Saika relation for Gaussian electron repulsion integrals","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":["quant-ph"],"primary_cat":"physics.chem-ph","authors_text":"Charles C. Forgy, David A. Mazziotti","submitted_at":"2026-06-30T19:42:12Z","abstract_excerpt":"The Obara-Saika (OS) method is one of the most widely used techniques in quantum chemistry for evaluating electron repulsion integrals (ERIs) via a set of recurrence relations that build higher angular momentum integrals from lower-order ones. The original derivation by Obara and Saika proceeded by directly relating integrals of differing angular momentum. In this work, we present a compact novel derivation of the OS vertical recurrence relation based solely on differential relations between Gaussian basis functions, expanding on a method suggested in earlier work. By explicitly deriving the r"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.00102","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/2607.00102/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":"2026-07-02T00:18:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"C9/E5znVyAynlEgxGGegBxFRmFoc/t7VcdELZvNRX4BDeHwBayp/1+fl+CSCKe8c3uBe4KG+miD942Fgf0F3Cg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-03T08:16:52.373949Z"},"content_sha256":"6480fb7f7a93312678f6bb55d58a8a3cbf31b953253b42ef2a5b93304e1f250d","schema_version":"1.0","event_id":"sha256:6480fb7f7a93312678f6bb55d58a8a3cbf31b953253b42ef2a5b93304e1f250d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5S5Z4X7JE5DNVLO2HUV74HHITW/bundle.json","state_url":"https://pith.science/pith/5S5Z4X7JE5DNVLO2HUV74HHITW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5S5Z4X7JE5DNVLO2HUV74HHITW/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":"2026-07-03T08:16:52Z","links":{"resolver":"https://pith.science/pith/5S5Z4X7JE5DNVLO2HUV74HHITW","bundle":"https://pith.science/pith/5S5Z4X7JE5DNVLO2HUV74HHITW/bundle.json","state":"https://pith.science/pith/5S5Z4X7JE5DNVLO2HUV74HHITW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5S5Z4X7JE5DNVLO2HUV74HHITW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:5S5Z4X7JE5DNVLO2HUV74HHITW","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":"2fa2226414e4191002a5c806dfc3fad87bac8e84bdf52006c336b20403e634ee","cross_cats_sorted":["quant-ph"],"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"physics.chem-ph","submitted_at":"2026-06-30T19:42:12Z","title_canon_sha256":"086fe6251482aaaa6ca9b08ee869391a90f70fe6fb7756a00b30671aeda6a388"},"schema_version":"1.0","source":{"id":"2607.00102","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.00102","created_at":"2026-07-02T00:18:34Z"},{"alias_kind":"arxiv_version","alias_value":"2607.00102v1","created_at":"2026-07-02T00:18:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.00102","created_at":"2026-07-02T00:18:34Z"},{"alias_kind":"pith_short_12","alias_value":"5S5Z4X7JE5DN","created_at":"2026-07-02T00:18:34Z"},{"alias_kind":"pith_short_16","alias_value":"5S5Z4X7JE5DNVLO2","created_at":"2026-07-02T00:18:34Z"},{"alias_kind":"pith_short_8","alias_value":"5S5Z4X7J","created_at":"2026-07-02T00:18:34Z"}],"graph_snapshots":[{"event_id":"sha256:6480fb7f7a93312678f6bb55d58a8a3cbf31b953253b42ef2a5b93304e1f250d","target":"graph","created_at":"2026-07-02T00:18:34Z","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/2607.00102/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The Obara-Saika (OS) method is one of the most widely used techniques in quantum chemistry for evaluating electron repulsion integrals (ERIs) via a set of recurrence relations that build higher angular momentum integrals from lower-order ones. The original derivation by Obara and Saika proceeded by directly relating integrals of differing angular momentum. In this work, we present a compact novel derivation of the OS vertical recurrence relation based solely on differential relations between Gaussian basis functions, expanding on a method suggested in earlier work. By explicitly deriving the r","authors_text":"Charles C. Forgy, David A. Mazziotti","cross_cats":["quant-ph"],"headline":"","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"physics.chem-ph","submitted_at":"2026-06-30T19:42:12Z","title":"A differential derivation of the Obara-Saika relation for Gaussian electron repulsion integrals"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.00102","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":"sha256:4c96eaed05f545e12882ca37ca116df94d6d223bf2fdab448948536c38505b61","target":"record","created_at":"2026-07-02T00:18:34Z","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":"2fa2226414e4191002a5c806dfc3fad87bac8e84bdf52006c336b20403e634ee","cross_cats_sorted":["quant-ph"],"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"physics.chem-ph","submitted_at":"2026-06-30T19:42:12Z","title_canon_sha256":"086fe6251482aaaa6ca9b08ee869391a90f70fe6fb7756a00b30671aeda6a388"},"schema_version":"1.0","source":{"id":"2607.00102","kind":"arxiv","version":1}},"canonical_sha256":"ecbb9e5fe92746daadda3d2bfe1ce89d9de1411bfa342494f1f06e2d2b5f1d52","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ecbb9e5fe92746daadda3d2bfe1ce89d9de1411bfa342494f1f06e2d2b5f1d52","first_computed_at":"2026-07-02T00:18:34.519441Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-02T00:18:34.519441Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Dz7OFqWcsCWotF/vYXAoX5C1to679Bj7beYOxfxJWqoHz3KulsTjbv9Bw833kHH8pJ3S4JPQjf4WGOb5prfxBg==","signature_status":"signed_v1","signed_at":"2026-07-02T00:18:34.519967Z","signed_message":"canonical_sha256_bytes"},"source_id":"2607.00102","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4c96eaed05f545e12882ca37ca116df94d6d223bf2fdab448948536c38505b61","sha256:6480fb7f7a93312678f6bb55d58a8a3cbf31b953253b42ef2a5b93304e1f250d"],"state_sha256":"a881d06041fe54224c634002d0c75b92f1280fbb74643a7f4eb55a3ce74189ee"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JnGMIwhd1Rry2IX8rvGjLPB7zL/FnrGnOYj0uHP0/asWChVvU7Z//2e4hFXJtPyY/8n943R4anmjTkHlixHtAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-03T08:16:52.376230Z","bundle_sha256":"10c219982186209458640bba1109383f54357d66a22c4047be6f534008142e80"}}