{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:7ACIEOXJV5ZMKIOLIAFSWY2GMY","short_pith_number":"pith:7ACIEOXJ","canonical_record":{"source":{"id":"1608.08272","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nucl-th","submitted_at":"2016-08-29T22:29:32Z","cross_cats_sorted":[],"title_canon_sha256":"0079180f45be44f59de39ff7b3d97465df323bbd89e5a9211151b2ead0689e2d","abstract_canon_sha256":"d41fcec9917f900092daf9a0088ac08753a05e0f3ea848f2ddc2699f3aed5022"},"schema_version":"1.0"},"canonical_sha256":"f804823ae9af72c521cb400b2b6346662bf38260a8089e6235333e3d16476868","source":{"kind":"arxiv","id":"1608.08272","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1608.08272","created_at":"2026-05-18T01:04:49Z"},{"alias_kind":"arxiv_version","alias_value":"1608.08272v2","created_at":"2026-05-18T01:04:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1608.08272","created_at":"2026-05-18T01:04:49Z"},{"alias_kind":"pith_short_12","alias_value":"7ACIEOXJV5ZM","created_at":"2026-05-18T12:30:04Z"},{"alias_kind":"pith_short_16","alias_value":"7ACIEOXJV5ZMKIOL","created_at":"2026-05-18T12:30:04Z"},{"alias_kind":"pith_short_8","alias_value":"7ACIEOXJ","created_at":"2026-05-18T12:30:04Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:7ACIEOXJV5ZMKIOLIAFSWY2GMY","target":"record","payload":{"canonical_record":{"source":{"id":"1608.08272","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nucl-th","submitted_at":"2016-08-29T22:29:32Z","cross_cats_sorted":[],"title_canon_sha256":"0079180f45be44f59de39ff7b3d97465df323bbd89e5a9211151b2ead0689e2d","abstract_canon_sha256":"d41fcec9917f900092daf9a0088ac08753a05e0f3ea848f2ddc2699f3aed5022"},"schema_version":"1.0"},"canonical_sha256":"f804823ae9af72c521cb400b2b6346662bf38260a8089e6235333e3d16476868","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:04:49.431156Z","signature_b64":"c/yYJh2kDfFwUxRaaRrdzEt9f/ZEQloM8lHhIDbej0vYhQGnpux32lDwjVI3evGBBKx8S6+hO5aCoH9/v/oKAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f804823ae9af72c521cb400b2b6346662bf38260a8089e6235333e3d16476868","last_reissued_at":"2026-05-18T01:04:49.430737Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:04:49.430737Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1608.08272","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:04:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"oOLRNy4Un59eP1iwLQzJCShJbVHcnEzE4YSJGrdG35AhAIQkfjcdmMdinvAkvlGBKgNEuMY3h5JITwS4sWN9BA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T10:26:58.395446Z"},"content_sha256":"e257a170593ca45904523bdbb81d5a7ed5eaffb050afe3e585a244a392f421c7","schema_version":"1.0","event_id":"sha256:e257a170593ca45904523bdbb81d5a7ed5eaffb050afe3e585a244a392f421c7"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:7ACIEOXJV5ZMKIOLIAFSWY2GMY","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Expectation Value of S(1).S(2)-Wave Functions Don't Matter","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"nucl-th","authors_text":"L. Zamick","submitted_at":"2016-08-29T22:29:32Z","abstract_excerpt":"We consider the expectation value of the quantity [3+ \\sigma (1).\\sigma (2)]/4 . This has a value +1 for 2 nucleons with spin S=1and zero for S=0. We show that for the jj coupling 2 particle configuration [j(1) j(2)]^{J} the expectation value has the structure A+B J(J+1) where A and B are constants. We then show that for a 2proton-2neutron configuration with total angular momentum I the expectation value per pair is independent of the details of the wave function and has a similar structure A' +B' I(I+1) with B'=B/6."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.08272","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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":"2026-05-18T01:04:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nqBVmR15d7D/XpmXvFXaqn7+JAHwlyyyWU/Sz6lINyujAn15DHhH87inisczqzztnxh54GNEAAaEPUDym8c0DA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T10:26:58.395806Z"},"content_sha256":"72d785d5486ba7284a6be8667b00a4d58b3d5b58e7df75d14319ef6dd0ee230d","schema_version":"1.0","event_id":"sha256:72d785d5486ba7284a6be8667b00a4d58b3d5b58e7df75d14319ef6dd0ee230d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7ACIEOXJV5ZMKIOLIAFSWY2GMY/bundle.json","state_url":"https://pith.science/pith/7ACIEOXJV5ZMKIOLIAFSWY2GMY/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7ACIEOXJV5ZMKIOLIAFSWY2GMY/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":"2026-06-22T10:26:58Z","links":{"resolver":"https://pith.science/pith/7ACIEOXJV5ZMKIOLIAFSWY2GMY","bundle":"https://pith.science/pith/7ACIEOXJV5ZMKIOLIAFSWY2GMY/bundle.json","state":"https://pith.science/pith/7ACIEOXJV5ZMKIOLIAFSWY2GMY/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7ACIEOXJV5ZMKIOLIAFSWY2GMY/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:7ACIEOXJV5ZMKIOLIAFSWY2GMY","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":"d41fcec9917f900092daf9a0088ac08753a05e0f3ea848f2ddc2699f3aed5022","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nucl-th","submitted_at":"2016-08-29T22:29:32Z","title_canon_sha256":"0079180f45be44f59de39ff7b3d97465df323bbd89e5a9211151b2ead0689e2d"},"schema_version":"1.0","source":{"id":"1608.08272","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1608.08272","created_at":"2026-05-18T01:04:49Z"},{"alias_kind":"arxiv_version","alias_value":"1608.08272v2","created_at":"2026-05-18T01:04:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1608.08272","created_at":"2026-05-18T01:04:49Z"},{"alias_kind":"pith_short_12","alias_value":"7ACIEOXJV5ZM","created_at":"2026-05-18T12:30:04Z"},{"alias_kind":"pith_short_16","alias_value":"7ACIEOXJV5ZMKIOL","created_at":"2026-05-18T12:30:04Z"},{"alias_kind":"pith_short_8","alias_value":"7ACIEOXJ","created_at":"2026-05-18T12:30:04Z"}],"graph_snapshots":[{"event_id":"sha256:72d785d5486ba7284a6be8667b00a4d58b3d5b58e7df75d14319ef6dd0ee230d","target":"graph","created_at":"2026-05-18T01:04:49Z","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"},"paper":{"abstract_excerpt":"We consider the expectation value of the quantity [3+ \\sigma (1).\\sigma (2)]/4 . This has a value +1 for 2 nucleons with spin S=1and zero for S=0. We show that for the jj coupling 2 particle configuration [j(1) j(2)]^{J} the expectation value has the structure A+B J(J+1) where A and B are constants. We then show that for a 2proton-2neutron configuration with total angular momentum I the expectation value per pair is independent of the details of the wave function and has a similar structure A' +B' I(I+1) with B'=B/6.","authors_text":"L. Zamick","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nucl-th","submitted_at":"2016-08-29T22:29:32Z","title":"The Expectation Value of S(1).S(2)-Wave Functions Don't Matter"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.08272","kind":"arxiv","version":2},"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:e257a170593ca45904523bdbb81d5a7ed5eaffb050afe3e585a244a392f421c7","target":"record","created_at":"2026-05-18T01:04:49Z","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":"d41fcec9917f900092daf9a0088ac08753a05e0f3ea848f2ddc2699f3aed5022","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nucl-th","submitted_at":"2016-08-29T22:29:32Z","title_canon_sha256":"0079180f45be44f59de39ff7b3d97465df323bbd89e5a9211151b2ead0689e2d"},"schema_version":"1.0","source":{"id":"1608.08272","kind":"arxiv","version":2}},"canonical_sha256":"f804823ae9af72c521cb400b2b6346662bf38260a8089e6235333e3d16476868","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f804823ae9af72c521cb400b2b6346662bf38260a8089e6235333e3d16476868","first_computed_at":"2026-05-18T01:04:49.430737Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:04:49.430737Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"c/yYJh2kDfFwUxRaaRrdzEt9f/ZEQloM8lHhIDbej0vYhQGnpux32lDwjVI3evGBBKx8S6+hO5aCoH9/v/oKAg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:04:49.431156Z","signed_message":"canonical_sha256_bytes"},"source_id":"1608.08272","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e257a170593ca45904523bdbb81d5a7ed5eaffb050afe3e585a244a392f421c7","sha256:72d785d5486ba7284a6be8667b00a4d58b3d5b58e7df75d14319ef6dd0ee230d"],"state_sha256":"9543bda22a61f6456459d504419351857b806c51c7c3766628f0fa83f13ae8db"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CERoqmNMxuUrtxQVy34zJHEKLp8M8ryT8u49vPwwxGUSStuP0qtx+LKFypRQXKVx7WvwgTObImfHOfs+rhomCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-22T10:26:58.397874Z","bundle_sha256":"ea74cd090707a824772f0dff9fb9dc2ba13d6b05ef6f267d9c2c33578f341556"}}