{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2007:SUEYKLM473BFQ6IV663IVD4YBE","short_pith_number":"pith:SUEYKLM4","canonical_record":{"source":{"id":"q-bio/0703032","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-bio.QM","submitted_at":"2007-03-14T19:03:30Z","cross_cats_sorted":["cond-mat.stat-mech","physics.bio-ph","q-bio.BM"],"title_canon_sha256":"75f08077804f8796d0e4243258427c5ed2da44e7ad3648d496ec17eb11f23289","abstract_canon_sha256":"4fbf0b93ecf3e8f9f03769f050f90fbc2c46f2f71c59bf000aac940eedc2f85d"},"schema_version":"1.0"},"canonical_sha256":"9509852d9cfec2587915f7b68a8f9809064f85aad068bcf1b726b252890eccfb","source":{"kind":"arxiv","id":"q-bio/0703032","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"q-bio/0703032","created_at":"2026-05-18T04:34:54Z"},{"alias_kind":"arxiv_version","alias_value":"q-bio/0703032v3","created_at":"2026-05-18T04:34:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.q-bio/0703032","created_at":"2026-05-18T04:34:54Z"},{"alias_kind":"pith_short_12","alias_value":"SUEYKLM473BF","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_16","alias_value":"SUEYKLM473BFQ6IV","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_8","alias_value":"SUEYKLM4","created_at":"2026-05-18T12:25:56Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2007:SUEYKLM473BFQ6IV663IVD4YBE","target":"record","payload":{"canonical_record":{"source":{"id":"q-bio/0703032","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-bio.QM","submitted_at":"2007-03-14T19:03:30Z","cross_cats_sorted":["cond-mat.stat-mech","physics.bio-ph","q-bio.BM"],"title_canon_sha256":"75f08077804f8796d0e4243258427c5ed2da44e7ad3648d496ec17eb11f23289","abstract_canon_sha256":"4fbf0b93ecf3e8f9f03769f050f90fbc2c46f2f71c59bf000aac940eedc2f85d"},"schema_version":"1.0"},"canonical_sha256":"9509852d9cfec2587915f7b68a8f9809064f85aad068bcf1b726b252890eccfb","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:34:54.509720Z","signature_b64":"T2g1RdJIDZN0oMlGEIXxtI43Uai4fy3JVAvJOByWm8HW/FyDNHDDSR7MUpQUiQTdaIuEwsOHRdXdAOUpSyhQDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9509852d9cfec2587915f7b68a8f9809064f85aad068bcf1b726b252890eccfb","last_reissued_at":"2026-05-18T04:34:54.509261Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:34:54.509261Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"q-bio/0703032","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:34:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VCQyf2a68kuJvCKIOJbR5u0KdeXWMB3uslYEmEfGK4DGo9YlAHn+7+cSfbt2mrgdM9r7dddVmTRcrowaUKiQDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T21:34:48.634885Z"},"content_sha256":"b6eaf9e133216c67fb56d18aa11ae5b59ffb0506452930b24939b531a109c9eb","schema_version":"1.0","event_id":"sha256:b6eaf9e133216c67fb56d18aa11ae5b59ffb0506452930b24939b531a109c9eb"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2007:SUEYKLM473BFQ6IV663IVD4YBE","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Dynamics of Microtubule Instabilities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech","physics.bio-ph","q-bio.BM"],"primary_cat":"q-bio.QM","authors_text":"P. L. Krapivsky, S. Redner, T. Antal","submitted_at":"2007-03-14T19:03:30Z","abstract_excerpt":"We investigate the dynamics of an idealized model of microtubule growth that evolves by: (i) attachment of guanosine triphosphate (GTP) at rate lambda, (ii) conversion of GTP to guanosine diphosphate (GDP) at rate 1, and (iii) detachment of GDP at rate mu. As a function of these rates, a microtubule can grow steadily or its length can fluctuate wildly. For mu=0, we find the exact tubule and GTP cap length distributions, and power-law length distributions of GTP and GDP islands. For mu=infinity, we argue that the time between catastrophes, where the microtubule shrinks to zero length, scales as"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"q-bio/0703032","kind":"arxiv","version":3},"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":"2026-05-18T04:34:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7Mo0ABJJKBDu39X7pkJZ8YQ0qLsP16Dd5lLdDbfLI+SscK2M1PxTidgSeZa1dZOL2ehj0xg18gK7feZPIWREDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T21:34:48.635374Z"},"content_sha256":"48a67af663680e24063742f68d98857f1185181e1389942d8438b0f42ac43ef1","schema_version":"1.0","event_id":"sha256:48a67af663680e24063742f68d98857f1185181e1389942d8438b0f42ac43ef1"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/SUEYKLM473BFQ6IV663IVD4YBE/bundle.json","state_url":"https://pith.science/pith/SUEYKLM473BFQ6IV663IVD4YBE/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/SUEYKLM473BFQ6IV663IVD4YBE/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":"2026-06-25T21:34:48Z","links":{"resolver":"https://pith.science/pith/SUEYKLM473BFQ6IV663IVD4YBE","bundle":"https://pith.science/pith/SUEYKLM473BFQ6IV663IVD4YBE/bundle.json","state":"https://pith.science/pith/SUEYKLM473BFQ6IV663IVD4YBE/state.json","well_known_bundle":"https://pith.science/.well-known/pith/SUEYKLM473BFQ6IV663IVD4YBE/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2007:SUEYKLM473BFQ6IV663IVD4YBE","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":"4fbf0b93ecf3e8f9f03769f050f90fbc2c46f2f71c59bf000aac940eedc2f85d","cross_cats_sorted":["cond-mat.stat-mech","physics.bio-ph","q-bio.BM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-bio.QM","submitted_at":"2007-03-14T19:03:30Z","title_canon_sha256":"75f08077804f8796d0e4243258427c5ed2da44e7ad3648d496ec17eb11f23289"},"schema_version":"1.0","source":{"id":"q-bio/0703032","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"q-bio/0703032","created_at":"2026-05-18T04:34:54Z"},{"alias_kind":"arxiv_version","alias_value":"q-bio/0703032v3","created_at":"2026-05-18T04:34:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.q-bio/0703032","created_at":"2026-05-18T04:34:54Z"},{"alias_kind":"pith_short_12","alias_value":"SUEYKLM473BF","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_16","alias_value":"SUEYKLM473BFQ6IV","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_8","alias_value":"SUEYKLM4","created_at":"2026-05-18T12:25:56Z"}],"graph_snapshots":[{"event_id":"sha256:48a67af663680e24063742f68d98857f1185181e1389942d8438b0f42ac43ef1","target":"graph","created_at":"2026-05-18T04:34:54Z","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 investigate the dynamics of an idealized model of microtubule growth that evolves by: (i) attachment of guanosine triphosphate (GTP) at rate lambda, (ii) conversion of GTP to guanosine diphosphate (GDP) at rate 1, and (iii) detachment of GDP at rate mu. As a function of these rates, a microtubule can grow steadily or its length can fluctuate wildly. For mu=0, we find the exact tubule and GTP cap length distributions, and power-law length distributions of GTP and GDP islands. For mu=infinity, we argue that the time between catastrophes, where the microtubule shrinks to zero length, scales as","authors_text":"P. L. Krapivsky, S. Redner, T. Antal","cross_cats":["cond-mat.stat-mech","physics.bio-ph","q-bio.BM"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-bio.QM","submitted_at":"2007-03-14T19:03:30Z","title":"Dynamics of Microtubule Instabilities"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"q-bio/0703032","kind":"arxiv","version":3},"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:b6eaf9e133216c67fb56d18aa11ae5b59ffb0506452930b24939b531a109c9eb","target":"record","created_at":"2026-05-18T04:34:54Z","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":"4fbf0b93ecf3e8f9f03769f050f90fbc2c46f2f71c59bf000aac940eedc2f85d","cross_cats_sorted":["cond-mat.stat-mech","physics.bio-ph","q-bio.BM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-bio.QM","submitted_at":"2007-03-14T19:03:30Z","title_canon_sha256":"75f08077804f8796d0e4243258427c5ed2da44e7ad3648d496ec17eb11f23289"},"schema_version":"1.0","source":{"id":"q-bio/0703032","kind":"arxiv","version":3}},"canonical_sha256":"9509852d9cfec2587915f7b68a8f9809064f85aad068bcf1b726b252890eccfb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9509852d9cfec2587915f7b68a8f9809064f85aad068bcf1b726b252890eccfb","first_computed_at":"2026-05-18T04:34:54.509261Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:34:54.509261Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"T2g1RdJIDZN0oMlGEIXxtI43Uai4fy3JVAvJOByWm8HW/FyDNHDDSR7MUpQUiQTdaIuEwsOHRdXdAOUpSyhQDg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:34:54.509720Z","signed_message":"canonical_sha256_bytes"},"source_id":"q-bio/0703032","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b6eaf9e133216c67fb56d18aa11ae5b59ffb0506452930b24939b531a109c9eb","sha256:48a67af663680e24063742f68d98857f1185181e1389942d8438b0f42ac43ef1"],"state_sha256":"08492065da4473a6ecec568147a9279a8e9331d8e31fb9b420907b550f30c9b8"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WUcfPsjqMMDOi0ZPVl1xAYgOjM7wCNDmwF228aPwLDoZsnWBlyemRdJs1W0GuOb5p6gFLOUDLpL6Rnr67QN+Bg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-25T21:34:48.638013Z","bundle_sha256":"71f4a194a4c13c37d10c66b37cc04c6ce44c11ffe009c600cfc5c8bf2c437e06"}}