{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:CVLN5CZW3YQKIBOVX64477QN5G","short_pith_number":"pith:CVLN5CZW","canonical_record":{"source":{"id":"2606.07793","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.bio-ph","submitted_at":"2026-06-05T19:11:42Z","cross_cats_sorted":[],"title_canon_sha256":"d3ec95c5757febc237afbc515785a52b4c12563229deb14160c57c369cfe2ee6","abstract_canon_sha256":"74be453f876449a8da35c9cf5da1f4b255e972ff06d642067a5875cb4f8bd29f"},"schema_version":"1.0"},"canonical_sha256":"1556de8b36de20a405d5bfb9cffe0de9be35b824e812914dfe37fc7e7ce3b026","source":{"kind":"arxiv","id":"2606.07793","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.07793","created_at":"2026-06-09T01:04:52Z"},{"alias_kind":"arxiv_version","alias_value":"2606.07793v1","created_at":"2026-06-09T01:04:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.07793","created_at":"2026-06-09T01:04:52Z"},{"alias_kind":"pith_short_12","alias_value":"CVLN5CZW3YQK","created_at":"2026-06-09T01:04:52Z"},{"alias_kind":"pith_short_16","alias_value":"CVLN5CZW3YQKIBOV","created_at":"2026-06-09T01:04:52Z"},{"alias_kind":"pith_short_8","alias_value":"CVLN5CZW","created_at":"2026-06-09T01:04:52Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:CVLN5CZW3YQKIBOVX64477QN5G","target":"record","payload":{"canonical_record":{"source":{"id":"2606.07793","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.bio-ph","submitted_at":"2026-06-05T19:11:42Z","cross_cats_sorted":[],"title_canon_sha256":"d3ec95c5757febc237afbc515785a52b4c12563229deb14160c57c369cfe2ee6","abstract_canon_sha256":"74be453f876449a8da35c9cf5da1f4b255e972ff06d642067a5875cb4f8bd29f"},"schema_version":"1.0"},"canonical_sha256":"1556de8b36de20a405d5bfb9cffe0de9be35b824e812914dfe37fc7e7ce3b026","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-09T01:04:52.339944Z","signature_b64":"IBCm8NFoQg+W4gtG9kA6fTg6FG0oqayrd4vcyxOF2qOsJ6FsJL0LNvdKP5SMR+jITzZ+cxd19MlIdAfFfhQZCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1556de8b36de20a405d5bfb9cffe0de9be35b824e812914dfe37fc7e7ce3b026","last_reissued_at":"2026-06-09T01:04:52.339489Z","signature_status":"signed_v1","first_computed_at":"2026-06-09T01:04:52.339489Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2606.07793","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":"2026-06-09T01:04:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZlC2UrlUESfAVObn+RR0XvsuxmDMAQUHVCg3lCjJX/NeQsF40Y1RQipWjxa42Tylw0B+Vb7eiqlocwKbetBsBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-03T19:29:05.597737Z"},"content_sha256":"ec344eb1299054a7835b57945eb6c6bc0ffb5bc1813a9d8e27a652034e9b14d6","schema_version":"1.0","event_id":"sha256:ec344eb1299054a7835b57945eb6c6bc0ffb5bc1813a9d8e27a652034e9b14d6"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:CVLN5CZW3YQKIBOVX64477QN5G","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Chemotactic Index for Spatial Gradient Sensing","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"physics.bio-ph","authors_text":"Nicholas A. Licata","submitted_at":"2026-06-05T19:11:42Z","abstract_excerpt":"We consider the problem of quantifying the chemotactic efficiency of single cells as measured by the chemotactic index $\\Psi$. Previous work in a model framework for direct sensing of spatial gradients indicated that $\\Psi$ depends on a single dimensionless group $s$, which plays the role of the square of the signal to noise ratio in the problem. We revisit this problem theoretically and demonstrate that the cumulants in the model can be calculated exactly. We derive explicit results for the multivariate cumulants up to third order in terms of the diffusive current density and Gaunt coefficien"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.07793","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/2606.07793/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":"2026-06-09T01:04:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5DO20rt/ozmHVml/tr1Hmdxo1ifttJ/kqL5ddXaCz+QlGSOEjvUgTqECPNfmMCE4TOUM8l3Hsd2ga+ETKR4vDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-03T19:29:05.598109Z"},"content_sha256":"2168eb428f28c9bbcc013730e3d9edbc98737fa15a17170c5686dced93e575bf","schema_version":"1.0","event_id":"sha256:2168eb428f28c9bbcc013730e3d9edbc98737fa15a17170c5686dced93e575bf"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/CVLN5CZW3YQKIBOVX64477QN5G/bundle.json","state_url":"https://pith.science/pith/CVLN5CZW3YQKIBOVX64477QN5G/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/CVLN5CZW3YQKIBOVX64477QN5G/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":"2026-07-03T19:29:05Z","links":{"resolver":"https://pith.science/pith/CVLN5CZW3YQKIBOVX64477QN5G","bundle":"https://pith.science/pith/CVLN5CZW3YQKIBOVX64477QN5G/bundle.json","state":"https://pith.science/pith/CVLN5CZW3YQKIBOVX64477QN5G/state.json","well_known_bundle":"https://pith.science/.well-known/pith/CVLN5CZW3YQKIBOVX64477QN5G/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:CVLN5CZW3YQKIBOVX64477QN5G","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":"74be453f876449a8da35c9cf5da1f4b255e972ff06d642067a5875cb4f8bd29f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.bio-ph","submitted_at":"2026-06-05T19:11:42Z","title_canon_sha256":"d3ec95c5757febc237afbc515785a52b4c12563229deb14160c57c369cfe2ee6"},"schema_version":"1.0","source":{"id":"2606.07793","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.07793","created_at":"2026-06-09T01:04:52Z"},{"alias_kind":"arxiv_version","alias_value":"2606.07793v1","created_at":"2026-06-09T01:04:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.07793","created_at":"2026-06-09T01:04:52Z"},{"alias_kind":"pith_short_12","alias_value":"CVLN5CZW3YQK","created_at":"2026-06-09T01:04:52Z"},{"alias_kind":"pith_short_16","alias_value":"CVLN5CZW3YQKIBOV","created_at":"2026-06-09T01:04:52Z"},{"alias_kind":"pith_short_8","alias_value":"CVLN5CZW","created_at":"2026-06-09T01:04:52Z"}],"graph_snapshots":[{"event_id":"sha256:2168eb428f28c9bbcc013730e3d9edbc98737fa15a17170c5686dced93e575bf","target":"graph","created_at":"2026-06-09T01:04:52Z","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/2606.07793/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We consider the problem of quantifying the chemotactic efficiency of single cells as measured by the chemotactic index $\\Psi$. Previous work in a model framework for direct sensing of spatial gradients indicated that $\\Psi$ depends on a single dimensionless group $s$, which plays the role of the square of the signal to noise ratio in the problem. We revisit this problem theoretically and demonstrate that the cumulants in the model can be calculated exactly. We derive explicit results for the multivariate cumulants up to third order in terms of the diffusive current density and Gaunt coefficien","authors_text":"Nicholas A. Licata","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.bio-ph","submitted_at":"2026-06-05T19:11:42Z","title":"The Chemotactic Index for Spatial Gradient Sensing"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.07793","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:ec344eb1299054a7835b57945eb6c6bc0ffb5bc1813a9d8e27a652034e9b14d6","target":"record","created_at":"2026-06-09T01:04:52Z","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":"74be453f876449a8da35c9cf5da1f4b255e972ff06d642067a5875cb4f8bd29f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.bio-ph","submitted_at":"2026-06-05T19:11:42Z","title_canon_sha256":"d3ec95c5757febc237afbc515785a52b4c12563229deb14160c57c369cfe2ee6"},"schema_version":"1.0","source":{"id":"2606.07793","kind":"arxiv","version":1}},"canonical_sha256":"1556de8b36de20a405d5bfb9cffe0de9be35b824e812914dfe37fc7e7ce3b026","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1556de8b36de20a405d5bfb9cffe0de9be35b824e812914dfe37fc7e7ce3b026","first_computed_at":"2026-06-09T01:04:52.339489Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-09T01:04:52.339489Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"IBCm8NFoQg+W4gtG9kA6fTg6FG0oqayrd4vcyxOF2qOsJ6FsJL0LNvdKP5SMR+jITzZ+cxd19MlIdAfFfhQZCw==","signature_status":"signed_v1","signed_at":"2026-06-09T01:04:52.339944Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.07793","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ec344eb1299054a7835b57945eb6c6bc0ffb5bc1813a9d8e27a652034e9b14d6","sha256:2168eb428f28c9bbcc013730e3d9edbc98737fa15a17170c5686dced93e575bf"],"state_sha256":"8052bd9faff532076d3e4adb85f10f97f879681c4d6554854149bcb5b0f9fc20"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YRBbcSU2hJWxseILq9ImppWytIl48U4SACUPuj5vdsQVgv4+m34t+lHHXazVT29XP3wpiatlu6SSNwHdt2e7Bg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-03T19:29:05.600177Z","bundle_sha256":"0fe3e30292c93b31e86ece973c98b3b69ce884a47c4244a3a76fb15254d7030d"}}