{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:7BIJBEQ7EYA4HHNAPNPWYAVHSE","short_pith_number":"pith:7BIJBEQ7","schema_version":"1.0","canonical_sha256":"f85090921f2601c39da07b5f6c02a7911f3477cbee3b92e2b55d5d6ee6987594","source":{"kind":"arxiv","id":"1901.08418","version":1},"attestation_state":"computed","paper":{"title":"Many-body contacts in fractal polymer chains and fBm trajectories","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.soft"],"primary_cat":"physics.chem-ph","authors_text":"K.E. Polovnikov, M.V. Tamm, S. Nechaev","submitted_at":"2019-01-24T14:16:21Z","abstract_excerpt":"We calculate the probabilities that a trajectory of a fractional Brownian motion with arbitrary fractal dimension $d_f$ visits the same spot $n \\ge 3$ times, at given moments $t_1, ..., t_n$, and obtain a determinant expression for these probabilities in terms of a displacement-displacement covariance matrix. Except for the standard Brownian trajectories with $d_f = 2$, the resulting many-body contact probabilities cannot be factorized into a product of single loop contributions. Within a Gaussian network model of a self-interacting polymer chain, which we suggested recently, the probabilities"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1901.08418","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.chem-ph","submitted_at":"2019-01-24T14:16:21Z","cross_cats_sorted":["cond-mat.soft"],"title_canon_sha256":"a32ccc74f59508c7d8ccfd30e674153815769e4dc163d90c70d0e7f53e9c80c8","abstract_canon_sha256":"a58001d80a9186562fe4094ddaf8682f94b8fb633a452110fed0920398af759b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:50:08.398137Z","signature_b64":"AOPQtUaowPqfFbD1J7FpqCZJhsaT3yN/zjZl/mdnwDBL9tZfLt73Ffa8d+WV+5/rqkwrW1BiG/ATbQmUHoUXAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f85090921f2601c39da07b5f6c02a7911f3477cbee3b92e2b55d5d6ee6987594","last_reissued_at":"2026-05-17T23:50:08.397618Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:50:08.397618Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Many-body contacts in fractal polymer chains and fBm trajectories","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.soft"],"primary_cat":"physics.chem-ph","authors_text":"K.E. Polovnikov, M.V. Tamm, S. Nechaev","submitted_at":"2019-01-24T14:16:21Z","abstract_excerpt":"We calculate the probabilities that a trajectory of a fractional Brownian motion with arbitrary fractal dimension $d_f$ visits the same spot $n \\ge 3$ times, at given moments $t_1, ..., t_n$, and obtain a determinant expression for these probabilities in terms of a displacement-displacement covariance matrix. Except for the standard Brownian trajectories with $d_f = 2$, the resulting many-body contact probabilities cannot be factorized into a product of single loop contributions. Within a Gaussian network model of a self-interacting polymer chain, which we suggested recently, the probabilities"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1901.08418","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1901.08418","created_at":"2026-05-17T23:50:08.397697+00:00"},{"alias_kind":"arxiv_version","alias_value":"1901.08418v1","created_at":"2026-05-17T23:50:08.397697+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1901.08418","created_at":"2026-05-17T23:50:08.397697+00:00"},{"alias_kind":"pith_short_12","alias_value":"7BIJBEQ7EYA4","created_at":"2026-05-18T12:33:12.712433+00:00"},{"alias_kind":"pith_short_16","alias_value":"7BIJBEQ7EYA4HHNA","created_at":"2026-05-18T12:33:12.712433+00:00"},{"alias_kind":"pith_short_8","alias_value":"7BIJBEQ7","created_at":"2026-05-18T12:33:12.712433+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/7BIJBEQ7EYA4HHNAPNPWYAVHSE","json":"https://pith.science/pith/7BIJBEQ7EYA4HHNAPNPWYAVHSE.json","graph_json":"https://pith.science/api/pith-number/7BIJBEQ7EYA4HHNAPNPWYAVHSE/graph.json","events_json":"https://pith.science/api/pith-number/7BIJBEQ7EYA4HHNAPNPWYAVHSE/events.json","paper":"https://pith.science/paper/7BIJBEQ7"},"agent_actions":{"view_html":"https://pith.science/pith/7BIJBEQ7EYA4HHNAPNPWYAVHSE","download_json":"https://pith.science/pith/7BIJBEQ7EYA4HHNAPNPWYAVHSE.json","view_paper":"https://pith.science/paper/7BIJBEQ7","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1901.08418&json=true","fetch_graph":"https://pith.science/api/pith-number/7BIJBEQ7EYA4HHNAPNPWYAVHSE/graph.json","fetch_events":"https://pith.science/api/pith-number/7BIJBEQ7EYA4HHNAPNPWYAVHSE/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/7BIJBEQ7EYA4HHNAPNPWYAVHSE/action/timestamp_anchor","attest_storage":"https://pith.science/pith/7BIJBEQ7EYA4HHNAPNPWYAVHSE/action/storage_attestation","attest_author":"https://pith.science/pith/7BIJBEQ7EYA4HHNAPNPWYAVHSE/action/author_attestation","sign_citation":"https://pith.science/pith/7BIJBEQ7EYA4HHNAPNPWYAVHSE/action/citation_signature","submit_replication":"https://pith.science/pith/7BIJBEQ7EYA4HHNAPNPWYAVHSE/action/replication_record"}},"created_at":"2026-05-17T23:50:08.397697+00:00","updated_at":"2026-05-17T23:50:08.397697+00:00"}