{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:QZQPUXXHYNC3S2IZAZXRMFDVTC","short_pith_number":"pith:QZQPUXXH","canonical_record":{"source":{"id":"1005.1444","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2010-05-10T04:15:40Z","cross_cats_sorted":["math-ph","math.MP","physics.chem-ph","physics.comp-ph"],"title_canon_sha256":"ef2788ad44c70a5a0144c8938ccb0a069cf2f254f96eb9881fff9593c7d8b4ae","abstract_canon_sha256":"cfe9251afeaf7fb805dc08267511eaa2507c14395b78f1e08e1998daef0d27fb"},"schema_version":"1.0"},"canonical_sha256":"8660fa5ee7c345b96919066f16147598a4fe611f5c743a9c0e1b79e1c2d3c1f8","source":{"kind":"arxiv","id":"1005.1444","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1005.1444","created_at":"2026-05-18T01:03:12Z"},{"alias_kind":"arxiv_version","alias_value":"1005.1444v1","created_at":"2026-05-18T01:03:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1005.1444","created_at":"2026-05-18T01:03:12Z"},{"alias_kind":"pith_short_12","alias_value":"QZQPUXXHYNC3","created_at":"2026-05-18T12:26:13Z"},{"alias_kind":"pith_short_16","alias_value":"QZQPUXXHYNC3S2IZ","created_at":"2026-05-18T12:26:13Z"},{"alias_kind":"pith_short_8","alias_value":"QZQPUXXH","created_at":"2026-05-18T12:26:13Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:QZQPUXXHYNC3S2IZAZXRMFDVTC","target":"record","payload":{"canonical_record":{"source":{"id":"1005.1444","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2010-05-10T04:15:40Z","cross_cats_sorted":["math-ph","math.MP","physics.chem-ph","physics.comp-ph"],"title_canon_sha256":"ef2788ad44c70a5a0144c8938ccb0a069cf2f254f96eb9881fff9593c7d8b4ae","abstract_canon_sha256":"cfe9251afeaf7fb805dc08267511eaa2507c14395b78f1e08e1998daef0d27fb"},"schema_version":"1.0"},"canonical_sha256":"8660fa5ee7c345b96919066f16147598a4fe611f5c743a9c0e1b79e1c2d3c1f8","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:03:12.273827Z","signature_b64":"fCKjQ74m82zFW2zsawHQSK0PzM+0mp7Y0JjJWQGXum6pbER+1U+2ZFLeS01W6bNwObu6afg4tTOP74qJKsyOAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8660fa5ee7c345b96919066f16147598a4fe611f5c743a9c0e1b79e1c2d3c1f8","last_reissued_at":"2026-05-18T01:03:12.273264Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:03:12.273264Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1005.1444","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":"2026-05-18T01:03:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"oez/7EPrdMEm15GbN5rsRm/M7NQXFWhgoz+gBhayp95uEvwxfp4tq8CTedUhCrlvDgTGwh9eCGwWKFS/ZcDLDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T18:18:06.664715Z"},"content_sha256":"fee78bf705e70d0f513b0e4aae0ae86d6331be1a4c0ed4aed872197d1ea6084d","schema_version":"1.0","event_id":"sha256:fee78bf705e70d0f513b0e4aae0ae86d6331be1a4c0ed4aed872197d1ea6084d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:QZQPUXXHYNC3S2IZAZXRMFDVTC","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Efficient implementation of the pivot algorithm for self-avoiding walks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP","physics.chem-ph","physics.comp-ph"],"primary_cat":"cond-mat.stat-mech","authors_text":"Nathan Clisby","submitted_at":"2010-05-10T04:15:40Z","abstract_excerpt":"The pivot algorithm for self-avoiding walks has been implemented in a manner which is dramatically faster than previous implementations, enabling extremely long walks to be efficiently simulated. We explicitly describe the data structures and algorithms used, and provide a heuristic argument that the mean time per attempted pivot for $N$-step self-avoiding walks is $O(1)$ for the square and simple cubic lattices. Numerical experiments conducted for self-avoiding walks with up to 268 million steps are consistent with $o(\\log N)$ behavior for the square lattice and $O(\\log N)$ behavior for the s"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1005.1444","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":"2026-05-18T01:03:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zOratOYboh28rpfXgqLV+9pTZWxU7ZrJO/a7eVdQKPp1h1xR9wxuaC7r/OTUEXv4Qbxo0F17Z+URzjAZEEveCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T18:18:06.665219Z"},"content_sha256":"3d7d678408517a4d4ef021eb80248b5f83bac7339fdff7c3a1b24222d64666f4","schema_version":"1.0","event_id":"sha256:3d7d678408517a4d4ef021eb80248b5f83bac7339fdff7c3a1b24222d64666f4"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QZQPUXXHYNC3S2IZAZXRMFDVTC/bundle.json","state_url":"https://pith.science/pith/QZQPUXXHYNC3S2IZAZXRMFDVTC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QZQPUXXHYNC3S2IZAZXRMFDVTC/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":"2026-06-01T18:18:06Z","links":{"resolver":"https://pith.science/pith/QZQPUXXHYNC3S2IZAZXRMFDVTC","bundle":"https://pith.science/pith/QZQPUXXHYNC3S2IZAZXRMFDVTC/bundle.json","state":"https://pith.science/pith/QZQPUXXHYNC3S2IZAZXRMFDVTC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QZQPUXXHYNC3S2IZAZXRMFDVTC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:QZQPUXXHYNC3S2IZAZXRMFDVTC","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":"cfe9251afeaf7fb805dc08267511eaa2507c14395b78f1e08e1998daef0d27fb","cross_cats_sorted":["math-ph","math.MP","physics.chem-ph","physics.comp-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2010-05-10T04:15:40Z","title_canon_sha256":"ef2788ad44c70a5a0144c8938ccb0a069cf2f254f96eb9881fff9593c7d8b4ae"},"schema_version":"1.0","source":{"id":"1005.1444","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1005.1444","created_at":"2026-05-18T01:03:12Z"},{"alias_kind":"arxiv_version","alias_value":"1005.1444v1","created_at":"2026-05-18T01:03:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1005.1444","created_at":"2026-05-18T01:03:12Z"},{"alias_kind":"pith_short_12","alias_value":"QZQPUXXHYNC3","created_at":"2026-05-18T12:26:13Z"},{"alias_kind":"pith_short_16","alias_value":"QZQPUXXHYNC3S2IZ","created_at":"2026-05-18T12:26:13Z"},{"alias_kind":"pith_short_8","alias_value":"QZQPUXXH","created_at":"2026-05-18T12:26:13Z"}],"graph_snapshots":[{"event_id":"sha256:3d7d678408517a4d4ef021eb80248b5f83bac7339fdff7c3a1b24222d64666f4","target":"graph","created_at":"2026-05-18T01:03:12Z","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":"The pivot algorithm for self-avoiding walks has been implemented in a manner which is dramatically faster than previous implementations, enabling extremely long walks to be efficiently simulated. We explicitly describe the data structures and algorithms used, and provide a heuristic argument that the mean time per attempted pivot for $N$-step self-avoiding walks is $O(1)$ for the square and simple cubic lattices. Numerical experiments conducted for self-avoiding walks with up to 268 million steps are consistent with $o(\\log N)$ behavior for the square lattice and $O(\\log N)$ behavior for the s","authors_text":"Nathan Clisby","cross_cats":["math-ph","math.MP","physics.chem-ph","physics.comp-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2010-05-10T04:15:40Z","title":"Efficient implementation of the pivot algorithm for self-avoiding walks"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1005.1444","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:fee78bf705e70d0f513b0e4aae0ae86d6331be1a4c0ed4aed872197d1ea6084d","target":"record","created_at":"2026-05-18T01:03:12Z","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":"cfe9251afeaf7fb805dc08267511eaa2507c14395b78f1e08e1998daef0d27fb","cross_cats_sorted":["math-ph","math.MP","physics.chem-ph","physics.comp-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2010-05-10T04:15:40Z","title_canon_sha256":"ef2788ad44c70a5a0144c8938ccb0a069cf2f254f96eb9881fff9593c7d8b4ae"},"schema_version":"1.0","source":{"id":"1005.1444","kind":"arxiv","version":1}},"canonical_sha256":"8660fa5ee7c345b96919066f16147598a4fe611f5c743a9c0e1b79e1c2d3c1f8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8660fa5ee7c345b96919066f16147598a4fe611f5c743a9c0e1b79e1c2d3c1f8","first_computed_at":"2026-05-18T01:03:12.273264Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:03:12.273264Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"fCKjQ74m82zFW2zsawHQSK0PzM+0mp7Y0JjJWQGXum6pbER+1U+2ZFLeS01W6bNwObu6afg4tTOP74qJKsyOAw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:03:12.273827Z","signed_message":"canonical_sha256_bytes"},"source_id":"1005.1444","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fee78bf705e70d0f513b0e4aae0ae86d6331be1a4c0ed4aed872197d1ea6084d","sha256:3d7d678408517a4d4ef021eb80248b5f83bac7339fdff7c3a1b24222d64666f4"],"state_sha256":"87eb10e895114a4152e37cccaa4e4d260ae4db4220a953a60f3858df3871a3b4"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SEf3YDxcFwf81iKMkj2/xoHcR5cw5YfDf6QWsfWneCSKHKf7UdUg5MaaquToDDmPcPSes54OWKANWsWwTX1hBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T18:18:06.667214Z","bundle_sha256":"b73afc8c2510be15ab4f7b5482690d6c8d945ed7e732197163e6c848e489e78d"}}