{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:YP2FQAK46JUTGKRBDPVWIFJNBR","short_pith_number":"pith:YP2FQAK4","canonical_record":{"source":{"id":"1908.02670","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"q-bio.PE","submitted_at":"2019-08-07T15:05:35Z","cross_cats_sorted":[],"title_canon_sha256":"604780e3af93ddbfbac91cd5ed0a7755ca8c84df4d6d798bcd9cb5dd0aa23333","abstract_canon_sha256":"bf87ebe6fe8c1fd5a3234c2ad4e583f673b749a6ae46fb3fd5312bb519d5384f"},"schema_version":"1.0"},"canonical_sha256":"c3f458015cf269332a211beb64152d0c68d026d69460f6706e34ed04fcd1cebf","source":{"kind":"arxiv","id":"1908.02670","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1908.02670","created_at":"2026-07-05T01:04:00Z"},{"alias_kind":"arxiv_version","alias_value":"1908.02670v2","created_at":"2026-07-05T01:04:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.02670","created_at":"2026-07-05T01:04:00Z"},{"alias_kind":"pith_short_12","alias_value":"YP2FQAK46JUT","created_at":"2026-07-05T01:04:00Z"},{"alias_kind":"pith_short_16","alias_value":"YP2FQAK46JUTGKRB","created_at":"2026-07-05T01:04:00Z"},{"alias_kind":"pith_short_8","alias_value":"YP2FQAK4","created_at":"2026-07-05T01:04:00Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:YP2FQAK46JUTGKRBDPVWIFJNBR","target":"record","payload":{"canonical_record":{"source":{"id":"1908.02670","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"q-bio.PE","submitted_at":"2019-08-07T15:05:35Z","cross_cats_sorted":[],"title_canon_sha256":"604780e3af93ddbfbac91cd5ed0a7755ca8c84df4d6d798bcd9cb5dd0aa23333","abstract_canon_sha256":"bf87ebe6fe8c1fd5a3234c2ad4e583f673b749a6ae46fb3fd5312bb519d5384f"},"schema_version":"1.0"},"canonical_sha256":"c3f458015cf269332a211beb64152d0c68d026d69460f6706e34ed04fcd1cebf","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T01:04:00.717046Z","signature_b64":"C/Oi14CcrMMtEz9riID/mGj5DM2blnRwUiAR+ua3oXjcaTjaPBICvFmrPmX2fQiizJ7V4DvMALq25arYV21/CA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c3f458015cf269332a211beb64152d0c68d026d69460f6706e34ed04fcd1cebf","last_reissued_at":"2026-07-05T01:04:00.716590Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T01:04:00.716590Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1908.02670","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T01:04:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/RigPIpUgemWfKwmn6u0y7YrnMwMHrTCrMMw/75suA1v2FwTJIFGnf/3MMhWdG8yL0UhrXcxVw/dPqVVms2UCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T15:56:41.387689Z"},"content_sha256":"3eaf370f5e17a45129e3d4f8a1313c350e3d1430ae56d009f9354541d7c9f1a0","schema_version":"1.0","event_id":"sha256:3eaf370f5e17a45129e3d4f8a1313c350e3d1430ae56d009f9354541d7c9f1a0"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:YP2FQAK46JUTGKRBDPVWIFJNBR","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Subpopulations and Stability in Microbial Communities","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"q-bio.PE","authors_text":"Nuno M. Oliveira, Pierre A. Haas, Raymond E. Goldstein","submitted_at":"2019-08-07T15:05:35Z","abstract_excerpt":"In microbial communities, each species often has multiple, distinct phenotypes, but studies of ecological stability have largely ignored this subpopulation structure. Here, we show that such implicit averaging over phenotypes leads to incorrect linear stability results. We then analyze the effect of phenotypic switching in detail in an asymptotic limit and partly overturn classical stability paradigms: abundant phenotypic variation is linearly destabilizing but, surprisingly, a rare phenotype such as bacterial persisters has a stabilizing effect. Finally, we extend these results by showing how"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.02670","kind":"arxiv","version":2},"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/1908.02670/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":"2026-07-05T01:04:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZUVJIDL6LvH9ZH2CLE82Gjj+7tvuobwJlYURASxjXIqD4jJUumZr0+XlVDDu9lLYzfVXpDp5cxSp+1Ez1nK0Cw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T15:56:41.388196Z"},"content_sha256":"6893236a97c81d369ab343539c6daa50c30e756b3334f39f31baedba58602d5a","schema_version":"1.0","event_id":"sha256:6893236a97c81d369ab343539c6daa50c30e756b3334f39f31baedba58602d5a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/YP2FQAK46JUTGKRBDPVWIFJNBR/bundle.json","state_url":"https://pith.science/pith/YP2FQAK46JUTGKRBDPVWIFJNBR/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/YP2FQAK46JUTGKRBDPVWIFJNBR/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":"2026-08-16T15:56:41Z","links":{"resolver":"https://pith.science/pith/YP2FQAK46JUTGKRBDPVWIFJNBR","bundle":"https://pith.science/pith/YP2FQAK46JUTGKRBDPVWIFJNBR/bundle.json","state":"https://pith.science/pith/YP2FQAK46JUTGKRBDPVWIFJNBR/state.json","well_known_bundle":"https://pith.science/.well-known/pith/YP2FQAK46JUTGKRBDPVWIFJNBR/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:YP2FQAK46JUTGKRBDPVWIFJNBR","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":"bf87ebe6fe8c1fd5a3234c2ad4e583f673b749a6ae46fb3fd5312bb519d5384f","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"q-bio.PE","submitted_at":"2019-08-07T15:05:35Z","title_canon_sha256":"604780e3af93ddbfbac91cd5ed0a7755ca8c84df4d6d798bcd9cb5dd0aa23333"},"schema_version":"1.0","source":{"id":"1908.02670","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1908.02670","created_at":"2026-07-05T01:04:00Z"},{"alias_kind":"arxiv_version","alias_value":"1908.02670v2","created_at":"2026-07-05T01:04:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.02670","created_at":"2026-07-05T01:04:00Z"},{"alias_kind":"pith_short_12","alias_value":"YP2FQAK46JUT","created_at":"2026-07-05T01:04:00Z"},{"alias_kind":"pith_short_16","alias_value":"YP2FQAK46JUTGKRB","created_at":"2026-07-05T01:04:00Z"},{"alias_kind":"pith_short_8","alias_value":"YP2FQAK4","created_at":"2026-07-05T01:04:00Z"}],"graph_snapshots":[{"event_id":"sha256:6893236a97c81d369ab343539c6daa50c30e756b3334f39f31baedba58602d5a","target":"graph","created_at":"2026-07-05T01:04:00Z","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/1908.02670/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In microbial communities, each species often has multiple, distinct phenotypes, but studies of ecological stability have largely ignored this subpopulation structure. Here, we show that such implicit averaging over phenotypes leads to incorrect linear stability results. We then analyze the effect of phenotypic switching in detail in an asymptotic limit and partly overturn classical stability paradigms: abundant phenotypic variation is linearly destabilizing but, surprisingly, a rare phenotype such as bacterial persisters has a stabilizing effect. Finally, we extend these results by showing how","authors_text":"Nuno M. Oliveira, Pierre A. Haas, Raymond E. Goldstein","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"q-bio.PE","submitted_at":"2019-08-07T15:05:35Z","title":"Subpopulations and Stability in Microbial Communities"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.02670","kind":"arxiv","version":2},"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":"sha256:3eaf370f5e17a45129e3d4f8a1313c350e3d1430ae56d009f9354541d7c9f1a0","target":"record","created_at":"2026-07-05T01:04:00Z","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":"bf87ebe6fe8c1fd5a3234c2ad4e583f673b749a6ae46fb3fd5312bb519d5384f","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"q-bio.PE","submitted_at":"2019-08-07T15:05:35Z","title_canon_sha256":"604780e3af93ddbfbac91cd5ed0a7755ca8c84df4d6d798bcd9cb5dd0aa23333"},"schema_version":"1.0","source":{"id":"1908.02670","kind":"arxiv","version":2}},"canonical_sha256":"c3f458015cf269332a211beb64152d0c68d026d69460f6706e34ed04fcd1cebf","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c3f458015cf269332a211beb64152d0c68d026d69460f6706e34ed04fcd1cebf","first_computed_at":"2026-07-05T01:04:00.716590Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T01:04:00.716590Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"C/Oi14CcrMMtEz9riID/mGj5DM2blnRwUiAR+ua3oXjcaTjaPBICvFmrPmX2fQiizJ7V4DvMALq25arYV21/CA==","signature_status":"signed_v1","signed_at":"2026-07-05T01:04:00.717046Z","signed_message":"canonical_sha256_bytes"},"source_id":"1908.02670","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3eaf370f5e17a45129e3d4f8a1313c350e3d1430ae56d009f9354541d7c9f1a0","sha256:6893236a97c81d369ab343539c6daa50c30e756b3334f39f31baedba58602d5a"],"state_sha256":"1450d838964ba7b908a032400c75773655280b4cd67314dc180e9bc986fcaa68"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"J/wGd7bkQge3iDZ+Yz7BdYrSNZeaWERmEqCbE39LErkzgN31URZM1btVp3Osx2rSrFf75I30al1wxp/Ewg+FCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-16T15:56:41.392250Z","bundle_sha256":"f9023e094b3e532ea079576417674037a3382c454aa5a497906d58699ab96fdf"}}