{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:SUMVT35VAYTQY5A4M3W27TWMXS","short_pith_number":"pith:SUMVT35V","canonical_record":{"source":{"id":"2606.22448","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-bio.QM","submitted_at":"2026-06-21T11:46:37Z","cross_cats_sorted":["cond-mat.stat-mech"],"title_canon_sha256":"85b7dfa3a3fb8eb2daeff93e6ddc9a70300f5c4929d27e144298baad7987181f","abstract_canon_sha256":"9e81c14188e0c4f5f7f9c46cdc46692d2b66a48f8bb51b330efdd39d4585af32"},"schema_version":"1.0"},"canonical_sha256":"951959efb506270c741c66edafceccbcba69612a725a825e172e06a6ba516851","source":{"kind":"arxiv","id":"2606.22448","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.22448","created_at":"2026-06-23T02:13:38Z"},{"alias_kind":"arxiv_version","alias_value":"2606.22448v1","created_at":"2026-06-23T02:13:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.22448","created_at":"2026-06-23T02:13:38Z"},{"alias_kind":"pith_short_12","alias_value":"SUMVT35VAYTQ","created_at":"2026-06-23T02:13:38Z"},{"alias_kind":"pith_short_16","alias_value":"SUMVT35VAYTQY5A4","created_at":"2026-06-23T02:13:38Z"},{"alias_kind":"pith_short_8","alias_value":"SUMVT35V","created_at":"2026-06-23T02:13:38Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:SUMVT35VAYTQY5A4M3W27TWMXS","target":"record","payload":{"canonical_record":{"source":{"id":"2606.22448","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-bio.QM","submitted_at":"2026-06-21T11:46:37Z","cross_cats_sorted":["cond-mat.stat-mech"],"title_canon_sha256":"85b7dfa3a3fb8eb2daeff93e6ddc9a70300f5c4929d27e144298baad7987181f","abstract_canon_sha256":"9e81c14188e0c4f5f7f9c46cdc46692d2b66a48f8bb51b330efdd39d4585af32"},"schema_version":"1.0"},"canonical_sha256":"951959efb506270c741c66edafceccbcba69612a725a825e172e06a6ba516851","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-23T02:13:38.651789Z","signature_b64":"LbRJBQERuI4knxg1hOVZxMAoqZcROrOFyPI6Nzflu1XfkvzavWlko+2oi7XnXLJHLqhP2lzuAd9YBRtwNFJFAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"951959efb506270c741c66edafceccbcba69612a725a825e172e06a6ba516851","last_reissued_at":"2026-06-23T02:13:38.651404Z","signature_status":"signed_v1","first_computed_at":"2026-06-23T02:13:38.651404Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2606.22448","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":"2026-06-23T02:13:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7HYoNlVHYJa7zqGZETO/eAxxR5c+Td8csXwi9sPbtyHKoAWFhdLAOMlj1hLyPgh4e84n7ThUR7TKTaNzOCwRBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-02T19:52:28.886368Z"},"content_sha256":"227d4b37168473224492ab77a9a524ae39a05d845f91a4caa852aea3903d48d3","schema_version":"1.0","event_id":"sha256:227d4b37168473224492ab77a9a524ae39a05d845f91a4caa852aea3903d48d3"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:SUMVT35VAYTQY5A4M3W27TWMXS","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Kinetics of template-directed multistate copolymerization","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech"],"primary_cat":"q-bio.QM","authors_text":"Pierre Gaspard","submitted_at":"2026-06-21T11:46:37Z","abstract_excerpt":"We consider processes of template-directed multistate copolymerization by molecular machines such as polymerases or ribosomes, having multiple states of conformation or activation. We show that the kinetic equations of these processes can be exactly solved for the mean growth velocity, the sequence probabilities of the grown copy, and the local probabilities and fractions of monomeric units in the copy. Asymptotically, in the long-time limit, the kinetic equations are solved with a matrix factorization ansatz in terms of a backward iteration, forming an iterated matrix function system, and a c"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.22448","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.22448/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-06-23T02:13:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jStX8ayfZeKfwvSr9dcgv4dfRSTqIKSVOBAL4oZPFJ9/BvHfX6uUQcenmLcC/vs7A051Noyao5M+5mJmjgHPBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-02T19:52:28.886752Z"},"content_sha256":"c6d77b03c6e65bdc74e9cf6d3ff37034bafbe3615fae0fac8143b48dbb463ebe","schema_version":"1.0","event_id":"sha256:c6d77b03c6e65bdc74e9cf6d3ff37034bafbe3615fae0fac8143b48dbb463ebe"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/SUMVT35VAYTQY5A4M3W27TWMXS/bundle.json","state_url":"https://pith.science/pith/SUMVT35VAYTQY5A4M3W27TWMXS/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/SUMVT35VAYTQY5A4M3W27TWMXS/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":"2026-07-02T19:52:28Z","links":{"resolver":"https://pith.science/pith/SUMVT35VAYTQY5A4M3W27TWMXS","bundle":"https://pith.science/pith/SUMVT35VAYTQY5A4M3W27TWMXS/bundle.json","state":"https://pith.science/pith/SUMVT35VAYTQY5A4M3W27TWMXS/state.json","well_known_bundle":"https://pith.science/.well-known/pith/SUMVT35VAYTQY5A4M3W27TWMXS/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:SUMVT35VAYTQY5A4M3W27TWMXS","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":"9e81c14188e0c4f5f7f9c46cdc46692d2b66a48f8bb51b330efdd39d4585af32","cross_cats_sorted":["cond-mat.stat-mech"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-bio.QM","submitted_at":"2026-06-21T11:46:37Z","title_canon_sha256":"85b7dfa3a3fb8eb2daeff93e6ddc9a70300f5c4929d27e144298baad7987181f"},"schema_version":"1.0","source":{"id":"2606.22448","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.22448","created_at":"2026-06-23T02:13:38Z"},{"alias_kind":"arxiv_version","alias_value":"2606.22448v1","created_at":"2026-06-23T02:13:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.22448","created_at":"2026-06-23T02:13:38Z"},{"alias_kind":"pith_short_12","alias_value":"SUMVT35VAYTQ","created_at":"2026-06-23T02:13:38Z"},{"alias_kind":"pith_short_16","alias_value":"SUMVT35VAYTQY5A4","created_at":"2026-06-23T02:13:38Z"},{"alias_kind":"pith_short_8","alias_value":"SUMVT35V","created_at":"2026-06-23T02:13:38Z"}],"graph_snapshots":[{"event_id":"sha256:c6d77b03c6e65bdc74e9cf6d3ff37034bafbe3615fae0fac8143b48dbb463ebe","target":"graph","created_at":"2026-06-23T02:13:38Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2606.22448/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We consider processes of template-directed multistate copolymerization by molecular machines such as polymerases or ribosomes, having multiple states of conformation or activation. We show that the kinetic equations of these processes can be exactly solved for the mean growth velocity, the sequence probabilities of the grown copy, and the local probabilities and fractions of monomeric units in the copy. Asymptotically, in the long-time limit, the kinetic equations are solved with a matrix factorization ansatz in terms of a backward iteration, forming an iterated matrix function system, and a c","authors_text":"Pierre Gaspard","cross_cats":["cond-mat.stat-mech"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-bio.QM","submitted_at":"2026-06-21T11:46:37Z","title":"Kinetics of template-directed multistate copolymerization"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.22448","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":"sha256:227d4b37168473224492ab77a9a524ae39a05d845f91a4caa852aea3903d48d3","target":"record","created_at":"2026-06-23T02:13:38Z","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":"9e81c14188e0c4f5f7f9c46cdc46692d2b66a48f8bb51b330efdd39d4585af32","cross_cats_sorted":["cond-mat.stat-mech"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-bio.QM","submitted_at":"2026-06-21T11:46:37Z","title_canon_sha256":"85b7dfa3a3fb8eb2daeff93e6ddc9a70300f5c4929d27e144298baad7987181f"},"schema_version":"1.0","source":{"id":"2606.22448","kind":"arxiv","version":1}},"canonical_sha256":"951959efb506270c741c66edafceccbcba69612a725a825e172e06a6ba516851","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"951959efb506270c741c66edafceccbcba69612a725a825e172e06a6ba516851","first_computed_at":"2026-06-23T02:13:38.651404Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-23T02:13:38.651404Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"LbRJBQERuI4knxg1hOVZxMAoqZcROrOFyPI6Nzflu1XfkvzavWlko+2oi7XnXLJHLqhP2lzuAd9YBRtwNFJFAg==","signature_status":"signed_v1","signed_at":"2026-06-23T02:13:38.651789Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.22448","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:227d4b37168473224492ab77a9a524ae39a05d845f91a4caa852aea3903d48d3","sha256:c6d77b03c6e65bdc74e9cf6d3ff37034bafbe3615fae0fac8143b48dbb463ebe"],"state_sha256":"3dec45e0d2110beda3a4cab2f507fcfe2c9b73d627eb895bfa8668354f052248"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"T3sq8zNZ5GL9xcUL38jZ42203mec2O1c7wB8zUcUWjl1I/L7SDG6E8TRGIKpug397fTnvVU5lUNxAhRjBS+pDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-02T19:52:28.888758Z","bundle_sha256":"d0d85b450bfe0ae1b459a94501d966337e3f9dce2b05c1c5c224b28d924d5b45"}}