{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:6JSR2PBTLRHEKSTYHXC3GCMYL3","short_pith_number":"pith:6JSR2PBT","canonical_record":{"source":{"id":"1511.03926","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.soft","submitted_at":"2015-11-12T15:29:44Z","cross_cats_sorted":[],"title_canon_sha256":"d9247da8fa52122f71cff75ed916ba6afd284cb63d3e02f930d53afcdf0a8dfc","abstract_canon_sha256":"aca2fc3b2d91945ad06aec3cf9d8aeff115476a423e88559d707c372e5b61581"},"schema_version":"1.0"},"canonical_sha256":"f2651d3c335c4e454a783dc5b309985ed979175f7850c9ae7f4596ca7fd24ba4","source":{"kind":"arxiv","id":"1511.03926","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1511.03926","created_at":"2026-05-18T01:17:11Z"},{"alias_kind":"arxiv_version","alias_value":"1511.03926v1","created_at":"2026-05-18T01:17:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1511.03926","created_at":"2026-05-18T01:17:11Z"},{"alias_kind":"pith_short_12","alias_value":"6JSR2PBTLRHE","created_at":"2026-05-18T12:29:07Z"},{"alias_kind":"pith_short_16","alias_value":"6JSR2PBTLRHEKSTY","created_at":"2026-05-18T12:29:07Z"},{"alias_kind":"pith_short_8","alias_value":"6JSR2PBT","created_at":"2026-05-18T12:29:07Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:6JSR2PBTLRHEKSTYHXC3GCMYL3","target":"record","payload":{"canonical_record":{"source":{"id":"1511.03926","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.soft","submitted_at":"2015-11-12T15:29:44Z","cross_cats_sorted":[],"title_canon_sha256":"d9247da8fa52122f71cff75ed916ba6afd284cb63d3e02f930d53afcdf0a8dfc","abstract_canon_sha256":"aca2fc3b2d91945ad06aec3cf9d8aeff115476a423e88559d707c372e5b61581"},"schema_version":"1.0"},"canonical_sha256":"f2651d3c335c4e454a783dc5b309985ed979175f7850c9ae7f4596ca7fd24ba4","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:17:11.493579Z","signature_b64":"ujU6QABTvLeo66IMQxJ3QkUCyWv9ZX6GUF4FpDH+8C8woYwtYA3ljU93O6JjveDsNBwvKq2MlcqBN0vmGeMGAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f2651d3c335c4e454a783dc5b309985ed979175f7850c9ae7f4596ca7fd24ba4","last_reissued_at":"2026-05-18T01:17:11.492961Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:17:11.492961Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1511.03926","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":"2026-05-18T01:17:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Oyfof8jkjGiroGNj3GViiXi1CQi0jhcr4Y1Pzov+kb3r+rprP5lx9cczUcaHEbpJ/E+dUPuZh4ortGhImUj9Cg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T19:13:30.140382Z"},"content_sha256":"b1282ec643e0315d5c09caaeed25ef1e86a1643cb4bf91b874c22648bb59ba26","schema_version":"1.0","event_id":"sha256:b1282ec643e0315d5c09caaeed25ef1e86a1643cb4bf91b874c22648bb59ba26"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:6JSR2PBTLRHEKSTYHXC3GCMYL3","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Loop formation in polymers in crowded environment","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cond-mat.soft","authors_text":"K. Haydukivska, V. Blavatska","submitted_at":"2015-11-12T15:29:44Z","abstract_excerpt":"We analyze the probability of a single loop formation in a long flexible polymer chain in disordered environment in $d$ dimensions. The structural defects are considered to be correlated on large distances $r$ according to a power law $\\sim r^{-a}$. Working within the frames of continuous chain model and applying the direct polymer renormalization scheme, we obtain the values of critical exponents governing the scaling of probabilities of loop formation with various positions along the chain as function of loops length. Our results quantitatively reveal that the presence of structural defects "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.03926","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":"2026-05-18T01:17:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"R8bXlDelEZd1/Y21yz5a+cJQ4z/+Vf/EyOXtuduOkXdofvOwa0AxU08YNB/Lyh+VP1fR19Z4ELbNi7ipfmwVAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T19:13:30.140720Z"},"content_sha256":"3b5bc7fcb1a34c687712ddf733ea6624c5d0d22ce96a452dec13752191c6d93c","schema_version":"1.0","event_id":"sha256:3b5bc7fcb1a34c687712ddf733ea6624c5d0d22ce96a452dec13752191c6d93c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6JSR2PBTLRHEKSTYHXC3GCMYL3/bundle.json","state_url":"https://pith.science/pith/6JSR2PBTLRHEKSTYHXC3GCMYL3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6JSR2PBTLRHEKSTYHXC3GCMYL3/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":"2026-05-28T19:13:30Z","links":{"resolver":"https://pith.science/pith/6JSR2PBTLRHEKSTYHXC3GCMYL3","bundle":"https://pith.science/pith/6JSR2PBTLRHEKSTYHXC3GCMYL3/bundle.json","state":"https://pith.science/pith/6JSR2PBTLRHEKSTYHXC3GCMYL3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6JSR2PBTLRHEKSTYHXC3GCMYL3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:6JSR2PBTLRHEKSTYHXC3GCMYL3","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":"aca2fc3b2d91945ad06aec3cf9d8aeff115476a423e88559d707c372e5b61581","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.soft","submitted_at":"2015-11-12T15:29:44Z","title_canon_sha256":"d9247da8fa52122f71cff75ed916ba6afd284cb63d3e02f930d53afcdf0a8dfc"},"schema_version":"1.0","source":{"id":"1511.03926","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1511.03926","created_at":"2026-05-18T01:17:11Z"},{"alias_kind":"arxiv_version","alias_value":"1511.03926v1","created_at":"2026-05-18T01:17:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1511.03926","created_at":"2026-05-18T01:17:11Z"},{"alias_kind":"pith_short_12","alias_value":"6JSR2PBTLRHE","created_at":"2026-05-18T12:29:07Z"},{"alias_kind":"pith_short_16","alias_value":"6JSR2PBTLRHEKSTY","created_at":"2026-05-18T12:29:07Z"},{"alias_kind":"pith_short_8","alias_value":"6JSR2PBT","created_at":"2026-05-18T12:29:07Z"}],"graph_snapshots":[{"event_id":"sha256:3b5bc7fcb1a34c687712ddf733ea6624c5d0d22ce96a452dec13752191c6d93c","target":"graph","created_at":"2026-05-18T01:17:11Z","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 analyze the probability of a single loop formation in a long flexible polymer chain in disordered environment in $d$ dimensions. The structural defects are considered to be correlated on large distances $r$ according to a power law $\\sim r^{-a}$. Working within the frames of continuous chain model and applying the direct polymer renormalization scheme, we obtain the values of critical exponents governing the scaling of probabilities of loop formation with various positions along the chain as function of loops length. Our results quantitatively reveal that the presence of structural defects ","authors_text":"K. Haydukivska, V. Blavatska","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.soft","submitted_at":"2015-11-12T15:29:44Z","title":"Loop formation in polymers in crowded environment"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.03926","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:b1282ec643e0315d5c09caaeed25ef1e86a1643cb4bf91b874c22648bb59ba26","target":"record","created_at":"2026-05-18T01:17:11Z","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":"aca2fc3b2d91945ad06aec3cf9d8aeff115476a423e88559d707c372e5b61581","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.soft","submitted_at":"2015-11-12T15:29:44Z","title_canon_sha256":"d9247da8fa52122f71cff75ed916ba6afd284cb63d3e02f930d53afcdf0a8dfc"},"schema_version":"1.0","source":{"id":"1511.03926","kind":"arxiv","version":1}},"canonical_sha256":"f2651d3c335c4e454a783dc5b309985ed979175f7850c9ae7f4596ca7fd24ba4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f2651d3c335c4e454a783dc5b309985ed979175f7850c9ae7f4596ca7fd24ba4","first_computed_at":"2026-05-18T01:17:11.492961Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:17:11.492961Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ujU6QABTvLeo66IMQxJ3QkUCyWv9ZX6GUF4FpDH+8C8woYwtYA3ljU93O6JjveDsNBwvKq2MlcqBN0vmGeMGAg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:17:11.493579Z","signed_message":"canonical_sha256_bytes"},"source_id":"1511.03926","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b1282ec643e0315d5c09caaeed25ef1e86a1643cb4bf91b874c22648bb59ba26","sha256:3b5bc7fcb1a34c687712ddf733ea6624c5d0d22ce96a452dec13752191c6d93c"],"state_sha256":"3307549d8990ff553d9c90e7b1145f487fd24cc08e385edc782bba62ca1cacb6"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"t4jFff62tYALnleeYxwUVaTi5PT0j3cONsWhFIJZuPJIjMGleEGGk/6exQSQRPCDdb9aLEu6l36J4M+HEPwjAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T19:13:30.142811Z","bundle_sha256":"d6d5d988d37b139f24f40157b33543585bf738e1668430e770944a5a63c3cfda"}}