{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:LZS27E7HNO2S2WXNTBKYXOG4EG","short_pith_number":"pith:LZS27E7H","canonical_record":{"source":{"id":"2607.29228","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.NE","submitted_at":"2026-07-31T09:58:58Z","cross_cats_sorted":["cs.AI"],"title_canon_sha256":"c55094a5b8625e70d0940fa3b5d153089b95939d475e96a6c799ac65d8b9ab45","abstract_canon_sha256":"8d17f0f4abfa782e57de55213616d523227764572e05477c07ab96305827ad7d"},"schema_version":"1.0"},"canonical_sha256":"5e65af93e76bb52d5aed98558bb8dc218d0b136389e429aaa660ca18ee80cd9d","source":{"kind":"arxiv","id":"2607.29228","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.29228","created_at":"2026-08-03T01:22:13Z"},{"alias_kind":"arxiv_version","alias_value":"2607.29228v1","created_at":"2026-08-03T01:22:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.29228","created_at":"2026-08-03T01:22:13Z"},{"alias_kind":"pith_short_12","alias_value":"LZS27E7HNO2S","created_at":"2026-08-03T01:22:13Z"},{"alias_kind":"pith_short_16","alias_value":"LZS27E7HNO2S2WXN","created_at":"2026-08-03T01:22:13Z"},{"alias_kind":"pith_short_8","alias_value":"LZS27E7H","created_at":"2026-08-03T01:22:13Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:LZS27E7HNO2S2WXNTBKYXOG4EG","target":"record","payload":{"canonical_record":{"source":{"id":"2607.29228","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.NE","submitted_at":"2026-07-31T09:58:58Z","cross_cats_sorted":["cs.AI"],"title_canon_sha256":"c55094a5b8625e70d0940fa3b5d153089b95939d475e96a6c799ac65d8b9ab45","abstract_canon_sha256":"8d17f0f4abfa782e57de55213616d523227764572e05477c07ab96305827ad7d"},"schema_version":"1.0"},"canonical_sha256":"5e65af93e76bb52d5aed98558bb8dc218d0b136389e429aaa660ca18ee80cd9d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-08-03T01:22:13.717872Z","signature_b64":"h8B67d/dkZ/oy1/ybswrpEALZMrNe6QQmaE4jdiMX0x+d2wCOKnGuw4kGKW2c5sTdPY9KsJoAtXHF8D+nKHDCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5e65af93e76bb52d5aed98558bb8dc218d0b136389e429aaa660ca18ee80cd9d","last_reissued_at":"2026-08-03T01:22:13.716316Z","signature_status":"signed_v1","first_computed_at":"2026-08-03T01:22:13.716316Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2607.29228","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":"2026-08-03T01:22:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0HTNNLVBK4ZBNqZY9gHrzgenjZwce6cMFjvMk3wIZxvkV/zjCRzBKhsNqGi+F5Q3OvvqkX7J5SPIO8cO5MXqDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-05T00:32:59.606271Z"},"content_sha256":"45b21df8866fd362509f749864b1846ffa8076147f07962dbd348ef6d0428a56","schema_version":"1.0","event_id":"sha256:45b21df8866fd362509f749864b1846ffa8076147f07962dbd348ef6d0428a56"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:LZS27E7HNO2S2WXNTBKYXOG4EG","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Linear Proposal Operators and Stochastic Search Geometry in SOMA and Differential Evolution","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.AI"],"primary_cat":"cs.NE","authors_text":"Ivan Zelinka, Vojt\\v{e}ch Nov\\'ak","submitted_at":"2026-07-31T09:58:58Z","abstract_excerpt":"Swarm and evolutionary algorithms are usually analyzed as complete procedural systems in which nonlinear selection, replacement, and adaptation obscure simpler structure within candidate generation. This paper introduces an operator--selection factorization that separates objective-independent variation from boundary repair and fitness-dependent selection, and uses it to study the proposal geometry of the Self-Organizing Migrating Algorithm (SOMA) and Differential Evolution (DE). The canonical SOMA proposal is shown to be affine in the search space and exactly linear in an augmented migrant--l"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.29228","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/2607.29228/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":"2026-08-03T01:22:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hyK3mq6OOf0oVGg26TuR1r4v8fSFaWRWTv+CNU7pKtPM9VbHQAjCjCK6qqNcU1vozHubHEH9N5kIaMvR8AzICg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-05T00:32:59.607132Z"},"content_sha256":"b82cdc9381e4f62777fd42db21efbfe4f8df4ba754c549a1f928c674f7b0da0f","schema_version":"1.0","event_id":"sha256:b82cdc9381e4f62777fd42db21efbfe4f8df4ba754c549a1f928c674f7b0da0f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/LZS27E7HNO2S2WXNTBKYXOG4EG/bundle.json","state_url":"https://pith.science/pith/LZS27E7HNO2S2WXNTBKYXOG4EG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/LZS27E7HNO2S2WXNTBKYXOG4EG/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":"2026-08-05T00:32:59Z","links":{"resolver":"https://pith.science/pith/LZS27E7HNO2S2WXNTBKYXOG4EG","bundle":"https://pith.science/pith/LZS27E7HNO2S2WXNTBKYXOG4EG/bundle.json","state":"https://pith.science/pith/LZS27E7HNO2S2WXNTBKYXOG4EG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/LZS27E7HNO2S2WXNTBKYXOG4EG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:LZS27E7HNO2S2WXNTBKYXOG4EG","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":"8d17f0f4abfa782e57de55213616d523227764572e05477c07ab96305827ad7d","cross_cats_sorted":["cs.AI"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.NE","submitted_at":"2026-07-31T09:58:58Z","title_canon_sha256":"c55094a5b8625e70d0940fa3b5d153089b95939d475e96a6c799ac65d8b9ab45"},"schema_version":"1.0","source":{"id":"2607.29228","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.29228","created_at":"2026-08-03T01:22:13Z"},{"alias_kind":"arxiv_version","alias_value":"2607.29228v1","created_at":"2026-08-03T01:22:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.29228","created_at":"2026-08-03T01:22:13Z"},{"alias_kind":"pith_short_12","alias_value":"LZS27E7HNO2S","created_at":"2026-08-03T01:22:13Z"},{"alias_kind":"pith_short_16","alias_value":"LZS27E7HNO2S2WXN","created_at":"2026-08-03T01:22:13Z"},{"alias_kind":"pith_short_8","alias_value":"LZS27E7H","created_at":"2026-08-03T01:22:13Z"}],"graph_snapshots":[{"event_id":"sha256:b82cdc9381e4f62777fd42db21efbfe4f8df4ba754c549a1f928c674f7b0da0f","target":"graph","created_at":"2026-08-03T01:22:13Z","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/2607.29228/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Swarm and evolutionary algorithms are usually analyzed as complete procedural systems in which nonlinear selection, replacement, and adaptation obscure simpler structure within candidate generation. This paper introduces an operator--selection factorization that separates objective-independent variation from boundary repair and fitness-dependent selection, and uses it to study the proposal geometry of the Self-Organizing Migrating Algorithm (SOMA) and Differential Evolution (DE). The canonical SOMA proposal is shown to be affine in the search space and exactly linear in an augmented migrant--l","authors_text":"Ivan Zelinka, Vojt\\v{e}ch Nov\\'ak","cross_cats":["cs.AI"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.NE","submitted_at":"2026-07-31T09:58:58Z","title":"Linear Proposal Operators and Stochastic Search Geometry in SOMA and Differential Evolution"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.29228","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":"sha256:45b21df8866fd362509f749864b1846ffa8076147f07962dbd348ef6d0428a56","target":"record","created_at":"2026-08-03T01:22:13Z","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":"8d17f0f4abfa782e57de55213616d523227764572e05477c07ab96305827ad7d","cross_cats_sorted":["cs.AI"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.NE","submitted_at":"2026-07-31T09:58:58Z","title_canon_sha256":"c55094a5b8625e70d0940fa3b5d153089b95939d475e96a6c799ac65d8b9ab45"},"schema_version":"1.0","source":{"id":"2607.29228","kind":"arxiv","version":1}},"canonical_sha256":"5e65af93e76bb52d5aed98558bb8dc218d0b136389e429aaa660ca18ee80cd9d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5e65af93e76bb52d5aed98558bb8dc218d0b136389e429aaa660ca18ee80cd9d","first_computed_at":"2026-08-03T01:22:13.716316Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-08-03T01:22:13.716316Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"h8B67d/dkZ/oy1/ybswrpEALZMrNe6QQmaE4jdiMX0x+d2wCOKnGuw4kGKW2c5sTdPY9KsJoAtXHF8D+nKHDCg==","signature_status":"signed_v1","signed_at":"2026-08-03T01:22:13.717872Z","signed_message":"canonical_sha256_bytes"},"source_id":"2607.29228","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:45b21df8866fd362509f749864b1846ffa8076147f07962dbd348ef6d0428a56","sha256:b82cdc9381e4f62777fd42db21efbfe4f8df4ba754c549a1f928c674f7b0da0f"],"state_sha256":"48881366857763b097721281f17091181252e98b222904dc7711948264c5c63b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PHR+blstpCbrkdjOnNZSzl5xcpkpqsQlCf/uULpynJI8ZxvOftmptwuP3Fm2RyeMGxd9P5cuIugoMJDqoyTkCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-05T00:32:59.612067Z","bundle_sha256":"db16d4fa384f677bdc1006be37cf9225f6ef9ebbd57e386093def043b37754ab"}}