{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:TJ5UZRTXOHTJMZSGHHOMUEBFIH","short_pith_number":"pith:TJ5UZRTX","canonical_record":{"source":{"id":"1312.6708","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.bio-ph","submitted_at":"2013-12-23T21:53:08Z","cross_cats_sorted":["q-bio.SC"],"title_canon_sha256":"4248aec140415dee11ae8b1de75b0c26b8d972314dc92a0c255a4671203b8104","abstract_canon_sha256":"3f5740911b198f0d0e60ba0a5067c13b7c6501b5c5a690187c0bc017fc4503cb"},"schema_version":"1.0"},"canonical_sha256":"9a7b4cc67771e696664639dcca102541df915f7dd14101da65aadbb3563a06a9","source":{"kind":"arxiv","id":"1312.6708","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1312.6708","created_at":"2026-05-18T01:45:42Z"},{"alias_kind":"arxiv_version","alias_value":"1312.6708v1","created_at":"2026-05-18T01:45:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1312.6708","created_at":"2026-05-18T01:45:42Z"},{"alias_kind":"pith_short_12","alias_value":"TJ5UZRTXOHTJ","created_at":"2026-05-18T12:28:02Z"},{"alias_kind":"pith_short_16","alias_value":"TJ5UZRTXOHTJMZSG","created_at":"2026-05-18T12:28:02Z"},{"alias_kind":"pith_short_8","alias_value":"TJ5UZRTX","created_at":"2026-05-18T12:28:02Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:TJ5UZRTXOHTJMZSGHHOMUEBFIH","target":"record","payload":{"canonical_record":{"source":{"id":"1312.6708","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.bio-ph","submitted_at":"2013-12-23T21:53:08Z","cross_cats_sorted":["q-bio.SC"],"title_canon_sha256":"4248aec140415dee11ae8b1de75b0c26b8d972314dc92a0c255a4671203b8104","abstract_canon_sha256":"3f5740911b198f0d0e60ba0a5067c13b7c6501b5c5a690187c0bc017fc4503cb"},"schema_version":"1.0"},"canonical_sha256":"9a7b4cc67771e696664639dcca102541df915f7dd14101da65aadbb3563a06a9","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:45:42.251770Z","signature_b64":"0jZL6HvrljeDbA9l9x7fpTz7fnlhQpQ9QRN7QN1Sjyhn4cB+DA7EcHnoywV1OlIZ640f6b17VwQ8h4Zkc1x0Cw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9a7b4cc67771e696664639dcca102541df915f7dd14101da65aadbb3563a06a9","last_reissued_at":"2026-05-18T01:45:42.251114Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:45:42.251114Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1312.6708","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":"2026-05-18T01:45:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ttR3LpYPqQCz5fsNBjLLJYyf3NLEo5hXIndvXmJZFSWN5T5gtv/0MxX+5pV44OaywDpZvhHhef5Bi6WRAioJCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T09:35:12.835469Z"},"content_sha256":"7c8e9d8eac11af9b7f9c40b9a28b9136bcc8a1b68b884c51746454ba88e1d77c","schema_version":"1.0","event_id":"sha256:7c8e9d8eac11af9b7f9c40b9a28b9136bcc8a1b68b884c51746454ba88e1d77c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:TJ5UZRTXOHTJMZSGHHOMUEBFIH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Development of Morphogen Gradient: The Role of Dimension and Discreteness","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["q-bio.SC"],"primary_cat":"physics.bio-ph","authors_text":"Anatoly B. Kolomeisky, Hamid Teimouri","submitted_at":"2013-12-23T21:53:08Z","abstract_excerpt":"The fundamental processes of biological development are governed by multiple signaling molecules that create non-uniform concentration profiles known as morphogen gradients. It is widely believed that the establishment of morphogen gradients is a result of complex processes that involve diffusion and degradation of locally produced signaling molecules. We developed a multi-dimensional discrete-state stochastic approach for investigating the corresponding reaction-diffusion models. It provided a full analytical description for stationary profiles and for important dynamic properties such as loc"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.6708","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":"2026-05-18T01:45:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/6u9dMflBWSiW+sRnEBfAEniPFIvOXA9/8hv3CyHuoU7d6i7cq0+3gQSfzX8+g2ooB5F7kqHon3fZT3PfFz9Ag==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T09:35:12.835819Z"},"content_sha256":"f6fbbc43df48005e1b88fd3864b5b1cdc5ade37a913a5e58695595ec95cdb924","schema_version":"1.0","event_id":"sha256:f6fbbc43df48005e1b88fd3864b5b1cdc5ade37a913a5e58695595ec95cdb924"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/TJ5UZRTXOHTJMZSGHHOMUEBFIH/bundle.json","state_url":"https://pith.science/pith/TJ5UZRTXOHTJMZSGHHOMUEBFIH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/TJ5UZRTXOHTJMZSGHHOMUEBFIH/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":"2026-06-01T09:35:12Z","links":{"resolver":"https://pith.science/pith/TJ5UZRTXOHTJMZSGHHOMUEBFIH","bundle":"https://pith.science/pith/TJ5UZRTXOHTJMZSGHHOMUEBFIH/bundle.json","state":"https://pith.science/pith/TJ5UZRTXOHTJMZSGHHOMUEBFIH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/TJ5UZRTXOHTJMZSGHHOMUEBFIH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:TJ5UZRTXOHTJMZSGHHOMUEBFIH","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":"3f5740911b198f0d0e60ba0a5067c13b7c6501b5c5a690187c0bc017fc4503cb","cross_cats_sorted":["q-bio.SC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.bio-ph","submitted_at":"2013-12-23T21:53:08Z","title_canon_sha256":"4248aec140415dee11ae8b1de75b0c26b8d972314dc92a0c255a4671203b8104"},"schema_version":"1.0","source":{"id":"1312.6708","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1312.6708","created_at":"2026-05-18T01:45:42Z"},{"alias_kind":"arxiv_version","alias_value":"1312.6708v1","created_at":"2026-05-18T01:45:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1312.6708","created_at":"2026-05-18T01:45:42Z"},{"alias_kind":"pith_short_12","alias_value":"TJ5UZRTXOHTJ","created_at":"2026-05-18T12:28:02Z"},{"alias_kind":"pith_short_16","alias_value":"TJ5UZRTXOHTJMZSG","created_at":"2026-05-18T12:28:02Z"},{"alias_kind":"pith_short_8","alias_value":"TJ5UZRTX","created_at":"2026-05-18T12:28:02Z"}],"graph_snapshots":[{"event_id":"sha256:f6fbbc43df48005e1b88fd3864b5b1cdc5ade37a913a5e58695595ec95cdb924","target":"graph","created_at":"2026-05-18T01:45:42Z","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 fundamental processes of biological development are governed by multiple signaling molecules that create non-uniform concentration profiles known as morphogen gradients. It is widely believed that the establishment of morphogen gradients is a result of complex processes that involve diffusion and degradation of locally produced signaling molecules. We developed a multi-dimensional discrete-state stochastic approach for investigating the corresponding reaction-diffusion models. It provided a full analytical description for stationary profiles and for important dynamic properties such as loc","authors_text":"Anatoly B. Kolomeisky, Hamid Teimouri","cross_cats":["q-bio.SC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.bio-ph","submitted_at":"2013-12-23T21:53:08Z","title":"Development of Morphogen Gradient: The Role of Dimension and Discreteness"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.6708","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":"sha256:7c8e9d8eac11af9b7f9c40b9a28b9136bcc8a1b68b884c51746454ba88e1d77c","target":"record","created_at":"2026-05-18T01:45:42Z","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":"3f5740911b198f0d0e60ba0a5067c13b7c6501b5c5a690187c0bc017fc4503cb","cross_cats_sorted":["q-bio.SC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.bio-ph","submitted_at":"2013-12-23T21:53:08Z","title_canon_sha256":"4248aec140415dee11ae8b1de75b0c26b8d972314dc92a0c255a4671203b8104"},"schema_version":"1.0","source":{"id":"1312.6708","kind":"arxiv","version":1}},"canonical_sha256":"9a7b4cc67771e696664639dcca102541df915f7dd14101da65aadbb3563a06a9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9a7b4cc67771e696664639dcca102541df915f7dd14101da65aadbb3563a06a9","first_computed_at":"2026-05-18T01:45:42.251114Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:45:42.251114Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"0jZL6HvrljeDbA9l9x7fpTz7fnlhQpQ9QRN7QN1Sjyhn4cB+DA7EcHnoywV1OlIZ640f6b17VwQ8h4Zkc1x0Cw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:45:42.251770Z","signed_message":"canonical_sha256_bytes"},"source_id":"1312.6708","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7c8e9d8eac11af9b7f9c40b9a28b9136bcc8a1b68b884c51746454ba88e1d77c","sha256:f6fbbc43df48005e1b88fd3864b5b1cdc5ade37a913a5e58695595ec95cdb924"],"state_sha256":"f2439e004823848f6ff9731255a6f9f3e2570f16a15ab1a7a2b4a642a3ba7c50"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KgN8RMht/DxytU602L/2aZeLu2Cr7LfOAFWrXdmsF/zNcp8GUJgVqECAf9GqQc1xvzwS2QSHYYiN/HCOlC7EDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T09:35:12.838016Z","bundle_sha256":"9cfd656d05784a39ed52b94fdbcfc1ce1aab35837adfe077ef453468a308099d"}}