{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:QSG2JWQURLKNSPG4WO5UXJE3ZU","short_pith_number":"pith:QSG2JWQU","canonical_record":{"source":{"id":"1301.7552","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.chem-ph","submitted_at":"2013-01-31T09:00:59Z","cross_cats_sorted":["cond-mat.other"],"title_canon_sha256":"c6135388cd62ff0f3032405cbc16e1e913a55617bda745085082459af807885a","abstract_canon_sha256":"0507bfc53b3b2b7de2f69f05e94c4ea918b619a013a1724e10049cbb917c2ab9"},"schema_version":"1.0"},"canonical_sha256":"848da4da148ad4d93cdcb3bb4ba49bcd23322c7cc8c9536485b084b47433573b","source":{"kind":"arxiv","id":"1301.7552","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1301.7552","created_at":"2026-05-18T01:51:56Z"},{"alias_kind":"arxiv_version","alias_value":"1301.7552v1","created_at":"2026-05-18T01:51:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1301.7552","created_at":"2026-05-18T01:51:56Z"},{"alias_kind":"pith_short_12","alias_value":"QSG2JWQURLKN","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_16","alias_value":"QSG2JWQURLKNSPG4","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_8","alias_value":"QSG2JWQU","created_at":"2026-05-18T12:27:57Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:QSG2JWQURLKNSPG4WO5UXJE3ZU","target":"record","payload":{"canonical_record":{"source":{"id":"1301.7552","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.chem-ph","submitted_at":"2013-01-31T09:00:59Z","cross_cats_sorted":["cond-mat.other"],"title_canon_sha256":"c6135388cd62ff0f3032405cbc16e1e913a55617bda745085082459af807885a","abstract_canon_sha256":"0507bfc53b3b2b7de2f69f05e94c4ea918b619a013a1724e10049cbb917c2ab9"},"schema_version":"1.0"},"canonical_sha256":"848da4da148ad4d93cdcb3bb4ba49bcd23322c7cc8c9536485b084b47433573b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:51:56.700083Z","signature_b64":"y8x/dXDX4Sc/e46qSRA0BPn+C1LKowZsmsc3BNVyzm8RRke9Jwmms43xHizaEtlkY+J6IKAjLwbckRM8z8DqDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"848da4da148ad4d93cdcb3bb4ba49bcd23322c7cc8c9536485b084b47433573b","last_reissued_at":"2026-05-18T01:51:56.699674Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:51:56.699674Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1301.7552","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":"2026-05-18T01:51:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GOkL0r0ShjGzlEGzWTF/Bg4iqNASSIMKGLA92PRa2A8qVtCLzaL/G10w5wtT0uQXu30tfX9DiDSi82SLiZW7Dg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T04:51:52.710075Z"},"content_sha256":"a85afbd1cc0c11a7fd84cd14843d6a5c07a740d3bad4ba41bb1c59886160f749","schema_version":"1.0","event_id":"sha256:a85afbd1cc0c11a7fd84cd14843d6a5c07a740d3bad4ba41bb1c59886160f749"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:QSG2JWQURLKNSPG4WO5UXJE3ZU","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Distribution of $r_{12} \\cdot p_{12}$ in quantum systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.other"],"primary_cat":"physics.chem-ph","authors_text":"Peter M. W. Gill, Pierre-Franc\\c{c}ois Loos, Yves A. Bernard","submitted_at":"2013-01-31T09:00:59Z","abstract_excerpt":"We introduce the two-particle probability density $X(x)$ of $x=\\bm{r}_{12}\\cdot\\bm{p}_{12}=\\left(\\bm{r}_1-\\bm{r}_2\\right) \\cdot \\left(\\bm{p}_1-\\bm{p}_2\\right)$. We show how to derive $X(x)$, which we call the Posmom intracule, from the many-particle wavefunction. We contrast it with the Dot intracule [Y. A. Bernard, D. L. Crittenden, P. M. W. Gill, Phys. Chem. Chem. Phys., 10, 3447 (2008)] which can be derived from the Wigner distribution and show the relationships between the Posmom intracule and the one-particle Posmom density [Y. A. Bernard, D. L. Crittenden, P. M. W .Gill, J.Phys. Chem.A, "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.7552","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":""},"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":"2026-05-18T01:51:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ldkTIf88l9/wf0EcR7hY5ElIQJ+xs6xt70qvQ/BpQVmOeZghC8Sbp5ky7Sr94CMIj7s2q1tV6JZkvHBaZKXTBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T04:51:52.710789Z"},"content_sha256":"42619054cf66f16bfbd6dabb8780da3e5979505b42e32e56e07492b34c4df025","schema_version":"1.0","event_id":"sha256:42619054cf66f16bfbd6dabb8780da3e5979505b42e32e56e07492b34c4df025"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QSG2JWQURLKNSPG4WO5UXJE3ZU/bundle.json","state_url":"https://pith.science/pith/QSG2JWQURLKNSPG4WO5UXJE3ZU/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QSG2JWQURLKNSPG4WO5UXJE3ZU/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":"2026-06-10T04:51:52Z","links":{"resolver":"https://pith.science/pith/QSG2JWQURLKNSPG4WO5UXJE3ZU","bundle":"https://pith.science/pith/QSG2JWQURLKNSPG4WO5UXJE3ZU/bundle.json","state":"https://pith.science/pith/QSG2JWQURLKNSPG4WO5UXJE3ZU/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QSG2JWQURLKNSPG4WO5UXJE3ZU/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:QSG2JWQURLKNSPG4WO5UXJE3ZU","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":"0507bfc53b3b2b7de2f69f05e94c4ea918b619a013a1724e10049cbb917c2ab9","cross_cats_sorted":["cond-mat.other"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.chem-ph","submitted_at":"2013-01-31T09:00:59Z","title_canon_sha256":"c6135388cd62ff0f3032405cbc16e1e913a55617bda745085082459af807885a"},"schema_version":"1.0","source":{"id":"1301.7552","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1301.7552","created_at":"2026-05-18T01:51:56Z"},{"alias_kind":"arxiv_version","alias_value":"1301.7552v1","created_at":"2026-05-18T01:51:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1301.7552","created_at":"2026-05-18T01:51:56Z"},{"alias_kind":"pith_short_12","alias_value":"QSG2JWQURLKN","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_16","alias_value":"QSG2JWQURLKNSPG4","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_8","alias_value":"QSG2JWQU","created_at":"2026-05-18T12:27:57Z"}],"graph_snapshots":[{"event_id":"sha256:42619054cf66f16bfbd6dabb8780da3e5979505b42e32e56e07492b34c4df025","target":"graph","created_at":"2026-05-18T01:51:56Z","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 introduce the two-particle probability density $X(x)$ of $x=\\bm{r}_{12}\\cdot\\bm{p}_{12}=\\left(\\bm{r}_1-\\bm{r}_2\\right) \\cdot \\left(\\bm{p}_1-\\bm{p}_2\\right)$. We show how to derive $X(x)$, which we call the Posmom intracule, from the many-particle wavefunction. We contrast it with the Dot intracule [Y. A. Bernard, D. L. Crittenden, P. M. W. Gill, Phys. Chem. Chem. Phys., 10, 3447 (2008)] which can be derived from the Wigner distribution and show the relationships between the Posmom intracule and the one-particle Posmom density [Y. A. Bernard, D. L. Crittenden, P. M. W .Gill, J.Phys. Chem.A, ","authors_text":"Peter M. W. Gill, Pierre-Franc\\c{c}ois Loos, Yves A. Bernard","cross_cats":["cond-mat.other"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.chem-ph","submitted_at":"2013-01-31T09:00:59Z","title":"Distribution of $r_{12} \\cdot p_{12}$ in quantum systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.7552","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:a85afbd1cc0c11a7fd84cd14843d6a5c07a740d3bad4ba41bb1c59886160f749","target":"record","created_at":"2026-05-18T01:51:56Z","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":"0507bfc53b3b2b7de2f69f05e94c4ea918b619a013a1724e10049cbb917c2ab9","cross_cats_sorted":["cond-mat.other"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.chem-ph","submitted_at":"2013-01-31T09:00:59Z","title_canon_sha256":"c6135388cd62ff0f3032405cbc16e1e913a55617bda745085082459af807885a"},"schema_version":"1.0","source":{"id":"1301.7552","kind":"arxiv","version":1}},"canonical_sha256":"848da4da148ad4d93cdcb3bb4ba49bcd23322c7cc8c9536485b084b47433573b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"848da4da148ad4d93cdcb3bb4ba49bcd23322c7cc8c9536485b084b47433573b","first_computed_at":"2026-05-18T01:51:56.699674Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:51:56.699674Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"y8x/dXDX4Sc/e46qSRA0BPn+C1LKowZsmsc3BNVyzm8RRke9Jwmms43xHizaEtlkY+J6IKAjLwbckRM8z8DqDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:51:56.700083Z","signed_message":"canonical_sha256_bytes"},"source_id":"1301.7552","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a85afbd1cc0c11a7fd84cd14843d6a5c07a740d3bad4ba41bb1c59886160f749","sha256:42619054cf66f16bfbd6dabb8780da3e5979505b42e32e56e07492b34c4df025"],"state_sha256":"3560130d7cbfaa053d3d1bd5e5602c4c942d1fcd52c06f764a82af0a04dd53cb"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wOFlzairAmcaj5l/rYtFlLWAlzoOiQxzYCKzcyaXgH2AwIIFj0HUuNhx46lSfbSf6+HCJ8wAvkGneX2Pp27jAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-10T04:51:52.714717Z","bundle_sha256":"646cbb82489781ed333a110f4849ae0442dbafc30f882634e036399898b7e19c"}}