{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:BDSCV52GPUEURQFDH3WARYHBFH","short_pith_number":"pith:BDSCV52G","canonical_record":{"source":{"id":"1802.05307","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2018-02-14T20:12:19Z","cross_cats_sorted":["math.MP","physics.bio-ph"],"title_canon_sha256":"681ee694134d8a2170120223c5ad43411ebb46c9f8bfc7774f81714ad8d8fc74","abstract_canon_sha256":"b6c1c26eded6c733c71c40c3e45d61cb88b3f147034be0d27cb8b557d2e56bed"},"schema_version":"1.0"},"canonical_sha256":"08e42af7467d0948c0a33eec08e0e129c40c419cb624ca36e529378a0a5a3ff7","source":{"kind":"arxiv","id":"1802.05307","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1802.05307","created_at":"2026-05-18T00:23:16Z"},{"alias_kind":"arxiv_version","alias_value":"1802.05307v1","created_at":"2026-05-18T00:23:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1802.05307","created_at":"2026-05-18T00:23:16Z"},{"alias_kind":"pith_short_12","alias_value":"BDSCV52GPUEU","created_at":"2026-05-18T12:32:13Z"},{"alias_kind":"pith_short_16","alias_value":"BDSCV52GPUEURQFD","created_at":"2026-05-18T12:32:13Z"},{"alias_kind":"pith_short_8","alias_value":"BDSCV52G","created_at":"2026-05-18T12:32:13Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:BDSCV52GPUEURQFDH3WARYHBFH","target":"record","payload":{"canonical_record":{"source":{"id":"1802.05307","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2018-02-14T20:12:19Z","cross_cats_sorted":["math.MP","physics.bio-ph"],"title_canon_sha256":"681ee694134d8a2170120223c5ad43411ebb46c9f8bfc7774f81714ad8d8fc74","abstract_canon_sha256":"b6c1c26eded6c733c71c40c3e45d61cb88b3f147034be0d27cb8b557d2e56bed"},"schema_version":"1.0"},"canonical_sha256":"08e42af7467d0948c0a33eec08e0e129c40c419cb624ca36e529378a0a5a3ff7","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:23:16.021026Z","signature_b64":"7/NemvYdnPzUEBxZVkxFgU/2kqiEjI7I++bdQ2d/a3NBqv1CFSPTjpFgM6jk4f9nx9SM3GqO0LOiGQTVzmYKAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"08e42af7467d0948c0a33eec08e0e129c40c419cb624ca36e529378a0a5a3ff7","last_reissued_at":"2026-05-18T00:23:16.020495Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:23:16.020495Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1802.05307","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":"2026-05-18T00:23:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lcgeg0EINklvc8uxLSe/ezMUOVWWycksF6nIe6KSd90PDF9DWnFLbqo2JN6Bg7hs/t+qj5n7z/85WC0BpzObAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T12:02:14.247101Z"},"content_sha256":"952dee4fee1a6f206427cb7677a42e2a36d706924cea52188c4891121469ab62","schema_version":"1.0","event_id":"sha256:952dee4fee1a6f206427cb7677a42e2a36d706924cea52188c4891121469ab62"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:BDSCV52GPUEURQFDH3WARYHBFH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Mean-field equation for a stochastic many-particle model of quorum-sensing microbial populations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP","physics.bio-ph"],"primary_cat":"math-ph","authors_text":"Erwin Frey, Johannes Knebel, Peter Pickl","submitted_at":"2018-02-14T20:12:19Z","abstract_excerpt":"We prove a mean-field equation for the dynamics of quorum-sensing microbial populations. In the stochastic many-particle process, individuals of a population produce public good molecules to different degrees. Individual production is metabolically costly such that non-producers replicate faster than producers. In addition, individuals sense the average production level in the well-mixed population and adjust their production in response (\"quorum sensing\"). Here we prove that the temporal evolution of such quorum-sensing populations converges to a macroscopic mean-field equation for increasing"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.05307","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":"2026-05-18T00:23:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6a+g/Ezauf7VdBhvkv0a/e99qRJklHMk4jgBDT6LTDBFCfJ1m7xlqp5JAQRNlP80wcW8MdhBHl1W1LgDj4TZCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T12:02:14.247467Z"},"content_sha256":"7da1dc3433cd1d179a293e26ccf74cb22b955ac44026e405236a8fe24ed47d45","schema_version":"1.0","event_id":"sha256:7da1dc3433cd1d179a293e26ccf74cb22b955ac44026e405236a8fe24ed47d45"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/BDSCV52GPUEURQFDH3WARYHBFH/bundle.json","state_url":"https://pith.science/pith/BDSCV52GPUEURQFDH3WARYHBFH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/BDSCV52GPUEURQFDH3WARYHBFH/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":"2026-06-01T12:02:14Z","links":{"resolver":"https://pith.science/pith/BDSCV52GPUEURQFDH3WARYHBFH","bundle":"https://pith.science/pith/BDSCV52GPUEURQFDH3WARYHBFH/bundle.json","state":"https://pith.science/pith/BDSCV52GPUEURQFDH3WARYHBFH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/BDSCV52GPUEURQFDH3WARYHBFH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:BDSCV52GPUEURQFDH3WARYHBFH","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":"b6c1c26eded6c733c71c40c3e45d61cb88b3f147034be0d27cb8b557d2e56bed","cross_cats_sorted":["math.MP","physics.bio-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2018-02-14T20:12:19Z","title_canon_sha256":"681ee694134d8a2170120223c5ad43411ebb46c9f8bfc7774f81714ad8d8fc74"},"schema_version":"1.0","source":{"id":"1802.05307","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1802.05307","created_at":"2026-05-18T00:23:16Z"},{"alias_kind":"arxiv_version","alias_value":"1802.05307v1","created_at":"2026-05-18T00:23:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1802.05307","created_at":"2026-05-18T00:23:16Z"},{"alias_kind":"pith_short_12","alias_value":"BDSCV52GPUEU","created_at":"2026-05-18T12:32:13Z"},{"alias_kind":"pith_short_16","alias_value":"BDSCV52GPUEURQFD","created_at":"2026-05-18T12:32:13Z"},{"alias_kind":"pith_short_8","alias_value":"BDSCV52G","created_at":"2026-05-18T12:32:13Z"}],"graph_snapshots":[{"event_id":"sha256:7da1dc3433cd1d179a293e26ccf74cb22b955ac44026e405236a8fe24ed47d45","target":"graph","created_at":"2026-05-18T00:23:16Z","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 prove a mean-field equation for the dynamics of quorum-sensing microbial populations. In the stochastic many-particle process, individuals of a population produce public good molecules to different degrees. Individual production is metabolically costly such that non-producers replicate faster than producers. In addition, individuals sense the average production level in the well-mixed population and adjust their production in response (\"quorum sensing\"). Here we prove that the temporal evolution of such quorum-sensing populations converges to a macroscopic mean-field equation for increasing","authors_text":"Erwin Frey, Johannes Knebel, Peter Pickl","cross_cats":["math.MP","physics.bio-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2018-02-14T20:12:19Z","title":"Mean-field equation for a stochastic many-particle model of quorum-sensing microbial populations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.05307","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":"sha256:952dee4fee1a6f206427cb7677a42e2a36d706924cea52188c4891121469ab62","target":"record","created_at":"2026-05-18T00:23:16Z","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":"b6c1c26eded6c733c71c40c3e45d61cb88b3f147034be0d27cb8b557d2e56bed","cross_cats_sorted":["math.MP","physics.bio-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2018-02-14T20:12:19Z","title_canon_sha256":"681ee694134d8a2170120223c5ad43411ebb46c9f8bfc7774f81714ad8d8fc74"},"schema_version":"1.0","source":{"id":"1802.05307","kind":"arxiv","version":1}},"canonical_sha256":"08e42af7467d0948c0a33eec08e0e129c40c419cb624ca36e529378a0a5a3ff7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"08e42af7467d0948c0a33eec08e0e129c40c419cb624ca36e529378a0a5a3ff7","first_computed_at":"2026-05-18T00:23:16.020495Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:23:16.020495Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"7/NemvYdnPzUEBxZVkxFgU/2kqiEjI7I++bdQ2d/a3NBqv1CFSPTjpFgM6jk4f9nx9SM3GqO0LOiGQTVzmYKAA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:23:16.021026Z","signed_message":"canonical_sha256_bytes"},"source_id":"1802.05307","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:952dee4fee1a6f206427cb7677a42e2a36d706924cea52188c4891121469ab62","sha256:7da1dc3433cd1d179a293e26ccf74cb22b955ac44026e405236a8fe24ed47d45"],"state_sha256":"dd91d72ec0a3266c07e902e18d5617fafd9383005ea2f445d2003ee30f748598"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"POnJMZW8UuQU8cBj0B/ISFzw97V7yTvbcFg4CxArwA1vWit+NqQjBwQmx2RddiEpbP/Yxm3QwSGB4NbbEh7bCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T12:02:14.249514Z","bundle_sha256":"9f79a8a4e39277d10bc69a16a7623f119ae2468572f5c7d85b8b76f87bbe8aab"}}