{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:LHQW6ZW3DYYXJ42HESFL3LYGJA","short_pith_number":"pith:LHQW6ZW3","canonical_record":{"source":{"id":"2607.07022","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2026-07-08T05:40:38Z","cross_cats_sorted":[],"title_canon_sha256":"497559820869616999b28b8cff88e0b9a91ccb72f2ce63e285a05025c74d26f2","abstract_canon_sha256":"e92501cffbeb69f37c6202b03034cfb34ad2b6506b61b085d1b247ec0c71bd8f"},"schema_version":"1.0"},"canonical_sha256":"59e16f66db1e3174f347248abdaf06480dbe98b23508b6452840dd72afd288ee","source":{"kind":"arxiv","id":"2607.07022","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.07022","created_at":"2026-07-09T01:20:12Z"},{"alias_kind":"arxiv_version","alias_value":"2607.07022v1","created_at":"2026-07-09T01:20:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.07022","created_at":"2026-07-09T01:20:12Z"},{"alias_kind":"pith_short_12","alias_value":"LHQW6ZW3DYYX","created_at":"2026-07-09T01:20:12Z"},{"alias_kind":"pith_short_16","alias_value":"LHQW6ZW3DYYXJ42H","created_at":"2026-07-09T01:20:12Z"},{"alias_kind":"pith_short_8","alias_value":"LHQW6ZW3","created_at":"2026-07-09T01:20:12Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:LHQW6ZW3DYYXJ42HESFL3LYGJA","target":"record","payload":{"canonical_record":{"source":{"id":"2607.07022","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2026-07-08T05:40:38Z","cross_cats_sorted":[],"title_canon_sha256":"497559820869616999b28b8cff88e0b9a91ccb72f2ce63e285a05025c74d26f2","abstract_canon_sha256":"e92501cffbeb69f37c6202b03034cfb34ad2b6506b61b085d1b247ec0c71bd8f"},"schema_version":"1.0"},"canonical_sha256":"59e16f66db1e3174f347248abdaf06480dbe98b23508b6452840dd72afd288ee","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-09T01:20:12.672332Z","signature_b64":"ibKL5cXxivv8CSD+fSPtF1yM/xY0uQB7WdYRQaisM89av09jTFigpHOvokbT11yHorf6yDQGKmNug/4hzRTsBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"59e16f66db1e3174f347248abdaf06480dbe98b23508b6452840dd72afd288ee","last_reissued_at":"2026-07-09T01:20:12.671960Z","signature_status":"signed_v1","first_computed_at":"2026-07-09T01:20:12.671960Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2607.07022","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":"2026-07-09T01:20:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"oRo3epcdAabnrWoTLLDbxQh4SSw0nlkPJw+OOnrt8YOwo5SJBQPsGdlplnFLWPjJpQf/ZQ/nlAlvwM3S+CfqBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-22T11:07:43.144195Z"},"content_sha256":"c94fe99f198b32e7ae9fc61da7e0eba20f1b4da1059645aecf6f162985497ef2","schema_version":"1.0","event_id":"sha256:c94fe99f198b32e7ae9fc61da7e0eba20f1b4da1059645aecf6f162985497ef2"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:LHQW6ZW3DYYXJ42HESFL3LYGJA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Coordinate-wise Elephant Random Walk","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Denisse A. Escobar Parra","submitted_at":"2026-07-08T05:40:38Z","abstract_excerpt":"We introduce a coordinate-wise version of the elephant random walk on the $k$-dimensional discrete hypercube $Q_k=\\{-1,1\\}^k$. At each global time step, one coordinate is selected uniformly at random and updated according to an elephant-type memory rule using only the past values of that coordinate. The resulting process is a nearest-neighbor walk with possible holding on the hypercube, but it is not Markovian on $Q_k$ because the transition probabilities depend on coordinate-wise empirical histories. We show that, when all memory parameters satisfy $p_i<1$, the coordinate-wise memory biases v"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.07022","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/2607.07022/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":"2026-07-09T01:20:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JkVRGxyXIEwHn/XG7/meXxBdUa9y0onq2S+NWUFkn4RjVt3/Def6STXRCj2fp3dueZMEgA3WLLiRWnPdz+cFCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-22T11:07:43.145211Z"},"content_sha256":"234a2628e7649b5ecb30d6a16728658f9486478216b452070884e2d468bbd83a","schema_version":"1.0","event_id":"sha256:234a2628e7649b5ecb30d6a16728658f9486478216b452070884e2d468bbd83a"},{"event_type":"integrity_finding","subject_pith_number":"pith:2026:LHQW6ZW3DYYXJ42HESFL3LYGJA","target":"integrity","payload":{"note":"Identifier '10.1214/07-ps122.url:https://doi.org/10.1214/07-ps122' is syntactically valid but the DOI registry (doi.org) returned 404, and Crossref / OpenAlex / internal corpus also have no record. The cited work could not be located through any authoritative source.","snippet":"WardWhitt.“ProofsofthemartingaleFCLT”.In:Probability Surveys4(2007),pp.268– 302.doi:10.1214/07-PS122.url:https://doi.org/10.1214/07-PS122","arxiv_id":"2607.07022","detector":"doi_compliance","evidence":{"doi":"10.1214/07-ps122.url:https://doi.org/10.1214/07-ps122","arxiv_id":null,"ref_index":15,"raw_excerpt":"WardWhitt.“ProofsofthemartingaleFCLT”.In:Probability Surveys4(2007),pp.268– 302.doi:10.1214/07-PS122.url:https://doi.org/10.1214/07-PS122","verdict_class":"cross_source","checked_sources":["crossref_by_doi","openalex_by_doi","doi_org_head"]},"severity":"critical","ref_index":15,"audited_at":"2026-07-09T21:39:42.437704Z","event_type":"pith.integrity.v1","detected_doi":"10.1214/07-ps122.url:https://doi.org/10.1214/07-ps122","detector_url":"https://pith.science/pith-integrity-protocol#doi_compliance","external_url":null,"finding_type":"unresolvable_identifier","evidence_hash":"e4cf7f46e3739dfc482e05c1c4fbbfe51a37bb9357b199b32405d7978cda6d48","paper_version":1,"verdict_class":"cross_source","resolved_title":null,"detector_version":"1.0.0","detected_arxiv_id":null,"integrity_event_id":10888,"payload_sha256":"9e08ec5e4de696509843b3863d2acbceb3c7c7105344ff1f83a39db057c4fd7d","signature_b64":"sIWRm4c77oi4b1SWVunaNaGykIayr80iGG+vb1jXh6skWodxYB1VUxYrkA4rsUD57ObaAgzvmTfiB7+S7fpCCg==","signing_key_id":"pith-v1-2026-05"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-09T21:43:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gv9XLu/lsXH+prAEcHcErcEh2ElUiURFtzIo5bsM5Xg7jEpfD+BaRTzKf9x7Y9CQdceQ9hYtxklwgh36OlQ+Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-22T11:07:43.149221Z"},"content_sha256":"6c9c31c2eacacf91bc60a5e7dac2b94d7670f26c481d79c0045d73de9d9148d9","schema_version":"1.0","event_id":"sha256:6c9c31c2eacacf91bc60a5e7dac2b94d7670f26c481d79c0045d73de9d9148d9"},{"event_type":"integrity_finding","subject_pith_number":"pith:2026:LHQW6ZW3DYYXJ42HESFL3LYGJA","target":"integrity","payload":{"note":"DOI in the printed bibliography is fragmented by whitespace or line breaks. A longer candidate (10.1103/PhysRevE.70.045101.url:https://link.aps.org/doi/10.1103/PhysRevE.70.045101) was visible in the surrounding text but could not be confirmed against doi.org as printed.","snippet":"Gunter M. Schütz and Steffen Trimper. “Elephants can always remember: Exact long- range memory effects in a non-Markovian random walk”. In:Physical Review E70.4 (2004), p. 045101.doi:10.1103/PhysRevE.70.045101.url:https://link.aps. org/doi/","arxiv_id":"2607.07022","detector":"doi_compliance","evidence":{"ref_index":12,"verdict_class":"incontrovertible","resolved_title":null,"printed_excerpt":"Gunter M. Schütz and Steffen Trimper. “Elephants can always remember: Exact long- range memory effects in a non-Markovian random walk”. In:Physical Review E70.4 (2004), p. 045101.doi:10.1103/PhysRevE.70.045101.url:https://link.aps. org/doi/","reconstructed_doi":"10.1103/PhysRevE.70.045101.url:https://link.aps.org/doi/10.1103/PhysRevE.70.045101"},"severity":"advisory","ref_index":12,"audited_at":"2026-07-09T21:39:42.437704Z","event_type":"pith.integrity.v1","detected_doi":"10.1103/PhysRevE.70.045101.url:https://link.aps.org/doi/10.1103/PhysRevE.70.045101","detector_url":"https://pith.science/pith-integrity-protocol#doi_compliance","external_url":null,"finding_type":"recoverable_identifier","evidence_hash":"b6360db682f25dc2627d05ff5536007e472f1421ec897d9a38d85e0897cc21f6","paper_version":1,"verdict_class":"incontrovertible","resolved_title":null,"detector_version":"1.0.0","detected_arxiv_id":null,"integrity_event_id":10887,"payload_sha256":"d335604ce191b107bc57ca8903177b3f30db5a3752eb3add9b05328c7223e4b1","signature_b64":"Z7zUFN2KxOGA559iL/+GYXtIJVx/nGhVuedhE4tjNZIRIhW5iwp+kQyxRzv9WYHe40sWEonZNv7/5gWU0RCBCw==","signing_key_id":"pith-v1-2026-05"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-09T21:43:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LuF+AVN9JKN0DGw+1Cc3siDesr1UlhSf1hfjVc40qKr7ZRjtBHZf+vM4Iq/J253ksuMXo8QsIbeyqVp0rB3vBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-22T11:07:43.149625Z"},"content_sha256":"efe5fcb8ca1ad36e1edb189b9aed558704ba7bacae0ad592d94f6200f6919980","schema_version":"1.0","event_id":"sha256:efe5fcb8ca1ad36e1edb189b9aed558704ba7bacae0ad592d94f6200f6919980"},{"event_type":"integrity_finding","subject_pith_number":"pith:2026:LHQW6ZW3DYYXJ42HESFL3LYGJA","target":"integrity","payload":{"note":"DOI in the printed bibliography is fragmented by whitespace or line breaks. A longer candidate (10.1515/eqc-2026-0017.url:https://doi.org/10.1515/eqc-2026-0017) was visible in the surrounding text but could not be confirmed against doi.org as printed.","snippet":"Lucile Laulin and Bastien Mallein. “Elephants Explore in Spirals Sometimes”. In: Stochastics and Quality Control().doi:doi:10.1515/eqc-2026-0017.url:https: //doi.org/10.1515/eqc-2026-0017","arxiv_id":"2607.07022","detector":"doi_compliance","evidence":{"ref_index":9,"verdict_class":"incontrovertible","resolved_title":null,"printed_excerpt":"Lucile Laulin and Bastien Mallein. “Elephants Explore in Spirals Sometimes”. In: Stochastics and Quality Control().doi:doi:10.1515/eqc-2026-0017.url:https: //doi.org/10.1515/eqc-2026-0017","reconstructed_doi":"10.1515/eqc-2026-0017.url:https://doi.org/10.1515/eqc-2026-0017"},"severity":"advisory","ref_index":9,"audited_at":"2026-07-09T21:39:42.437704Z","event_type":"pith.integrity.v1","detected_doi":"10.1515/eqc-2026-0017.url:https://doi.org/10.1515/eqc-2026-0017","detector_url":"https://pith.science/pith-integrity-protocol#doi_compliance","external_url":null,"finding_type":"recoverable_identifier","evidence_hash":"04c5a26469cd06b613b1ab6667b773fc46452d1ef4ba23ed3e5dcfb84437a435","paper_version":1,"verdict_class":"incontrovertible","resolved_title":null,"detector_version":"1.0.0","detected_arxiv_id":null,"integrity_event_id":10886,"payload_sha256":"9bb83b8ca5b0801ce5108dfbcefd40427a01d394eeb150176204a5fa14e6c2d5","signature_b64":"UDFAwWNGlpYMThZpDuoZR4SvXNlwKBHWpnumiFC4/u+5SlI1ay7JQg77PWdZmHlbVomJNb1oymaOVnnWXBvPDQ==","signing_key_id":"pith-v1-2026-05"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-09T21:43:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"iOdPRN1ZWyDciIqE3IdKkfNxPTLEXcjlpnvmjOXE00GNUB7Ds9PHg8BjQTw9WXRAAVgklOcyCsHhUPw0yi1vDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-22T11:07:43.149998Z"},"content_sha256":"6c279514268c9222b02ab6b4b3b713bb0b21a5c989bb4abe7098478205e03ad9","schema_version":"1.0","event_id":"sha256:6c279514268c9222b02ab6b4b3b713bb0b21a5c989bb4abe7098478205e03ad9"},{"event_type":"integrity_finding","subject_pith_number":"pith:2026:LHQW6ZW3DYYXJ42HESFL3LYGJA","target":"integrity","payload":{"note":"DOI in the printed bibliography is fragmented by whitespace or line breaks. A longer candidate (10.1063/1.4983566.url:https://doi.org/10.1063/1.4983566) was visible in the surrounding text but could not be confirmed against doi.org as printed.","snippet":"Cristian F. Coletti, Renato Gava, and Gunter M. Schütz. “Central limit theorem and related results for the elephant random walk”. In:Journal of Mathematical Physics58.5 (2017), p. 053303.doi:10.1063/1.4983566.url:https://doi.org/10.1063/1. ","arxiv_id":"2607.07022","detector":"doi_compliance","evidence":{"ref_index":6,"verdict_class":"incontrovertible","resolved_title":null,"printed_excerpt":"Cristian F. Coletti, Renato Gava, and Gunter M. Schütz. “Central limit theorem and related results for the elephant random walk”. In:Journal of Mathematical Physics58.5 (2017), p. 053303.doi:10.1063/1.4983566.url:https://doi.org/10.1063/1. ","reconstructed_doi":"10.1063/1.4983566.url:https://doi.org/10.1063/1.4983566"},"severity":"advisory","ref_index":6,"audited_at":"2026-07-09T21:39:42.437704Z","event_type":"pith.integrity.v1","detected_doi":"10.1063/1.4983566.url:https://doi.org/10.1063/1.4983566","detector_url":"https://pith.science/pith-integrity-protocol#doi_compliance","external_url":null,"finding_type":"recoverable_identifier","evidence_hash":"8edeac7ae84caa2a9a09cb734e2446dfca272df31543c9d435a20f2fcd6e48d7","paper_version":1,"verdict_class":"incontrovertible","resolved_title":null,"detector_version":"1.0.0","detected_arxiv_id":null,"integrity_event_id":10885,"payload_sha256":"1ce30ef5af1e3d77a028dbd08075e758ed5a416c11e1c3acfa9179f3cab473b6","signature_b64":"tfVYrz9w6/5dhhHxcV0NdhSlfN+nqLKvGDsArOXFQEnglDB3+uZWkh0ktkxylSzgbGuxwuCdbhO9RdnPC3SdAw==","signing_key_id":"pith-v1-2026-05"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-09T21:43:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"AJWeYnoGijyZG1Exrf4hLSA7/xciapaSajVEYrqowKH32fp6StG70FykNDIrXLaFfv/UZJZ793SgZzScNvXsCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-22T11:07:43.150380Z"},"content_sha256":"6611634f6d983fc3e21a7b5a20e6ddd9e4423d73db628d319b0bc531ccabf0b2","schema_version":"1.0","event_id":"sha256:6611634f6d983fc3e21a7b5a20e6ddd9e4423d73db628d319b0bc531ccabf0b2"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/LHQW6ZW3DYYXJ42HESFL3LYGJA/bundle.json","state_url":"https://pith.science/pith/LHQW6ZW3DYYXJ42HESFL3LYGJA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/LHQW6ZW3DYYXJ42HESFL3LYGJA/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":"2026-08-22T11:07:43Z","links":{"resolver":"https://pith.science/pith/LHQW6ZW3DYYXJ42HESFL3LYGJA","bundle":"https://pith.science/pith/LHQW6ZW3DYYXJ42HESFL3LYGJA/bundle.json","state":"https://pith.science/pith/LHQW6ZW3DYYXJ42HESFL3LYGJA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/LHQW6ZW3DYYXJ42HESFL3LYGJA/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:LHQW6ZW3DYYXJ42HESFL3LYGJA","merge_version":"pith-open-graph-merge-v1","event_count":6,"valid_event_count":6,"invalid_event_count":0,"equivocation_count":1,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"e92501cffbeb69f37c6202b03034cfb34ad2b6506b61b085d1b247ec0c71bd8f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2026-07-08T05:40:38Z","title_canon_sha256":"497559820869616999b28b8cff88e0b9a91ccb72f2ce63e285a05025c74d26f2"},"schema_version":"1.0","source":{"id":"2607.07022","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.07022","created_at":"2026-07-09T01:20:12Z"},{"alias_kind":"arxiv_version","alias_value":"2607.07022v1","created_at":"2026-07-09T01:20:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.07022","created_at":"2026-07-09T01:20:12Z"},{"alias_kind":"pith_short_12","alias_value":"LHQW6ZW3DYYX","created_at":"2026-07-09T01:20:12Z"},{"alias_kind":"pith_short_16","alias_value":"LHQW6ZW3DYYXJ42H","created_at":"2026-07-09T01:20:12Z"},{"alias_kind":"pith_short_8","alias_value":"LHQW6ZW3","created_at":"2026-07-09T01:20:12Z"}],"graph_snapshots":[{"event_id":"sha256:234a2628e7649b5ecb30d6a16728658f9486478216b452070884e2d468bbd83a","target":"graph","created_at":"2026-07-09T01:20:12Z","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/2607.07022/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We introduce a coordinate-wise version of the elephant random walk on the $k$-dimensional discrete hypercube $Q_k=\\{-1,1\\}^k$. At each global time step, one coordinate is selected uniformly at random and updated according to an elephant-type memory rule using only the past values of that coordinate. The resulting process is a nearest-neighbor walk with possible holding on the hypercube, but it is not Markovian on $Q_k$ because the transition probabilities depend on coordinate-wise empirical histories. We show that, when all memory parameters satisfy $p_i<1$, the coordinate-wise memory biases v","authors_text":"Denisse A. Escobar Parra","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2026-07-08T05:40:38Z","title":"Coordinate-wise Elephant Random Walk"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.07022","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:c94fe99f198b32e7ae9fc61da7e0eba20f1b4da1059645aecf6f162985497ef2","target":"record","created_at":"2026-07-09T01:20:12Z","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":"e92501cffbeb69f37c6202b03034cfb34ad2b6506b61b085d1b247ec0c71bd8f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2026-07-08T05:40:38Z","title_canon_sha256":"497559820869616999b28b8cff88e0b9a91ccb72f2ce63e285a05025c74d26f2"},"schema_version":"1.0","source":{"id":"2607.07022","kind":"arxiv","version":1}},"canonical_sha256":"59e16f66db1e3174f347248abdaf06480dbe98b23508b6452840dd72afd288ee","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"59e16f66db1e3174f347248abdaf06480dbe98b23508b6452840dd72afd288ee","first_computed_at":"2026-07-09T01:20:12.671960Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-09T01:20:12.671960Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ibKL5cXxivv8CSD+fSPtF1yM/xY0uQB7WdYRQaisM89av09jTFigpHOvokbT11yHorf6yDQGKmNug/4hzRTsBg==","signature_status":"signed_v1","signed_at":"2026-07-09T01:20:12.672332Z","signed_message":"canonical_sha256_bytes"},"source_id":"2607.07022","source_kind":"arxiv","source_version":1}}},"equivocations":[{"signer_id":"pith.science","event_type":"integrity_finding","target":"integrity","event_ids":["sha256:6611634f6d983fc3e21a7b5a20e6ddd9e4423d73db628d319b0bc531ccabf0b2","sha256:6c279514268c9222b02ab6b4b3b713bb0b21a5c989bb4abe7098478205e03ad9","sha256:6c9c31c2eacacf91bc60a5e7dac2b94d7670f26c481d79c0045d73de9d9148d9","sha256:efe5fcb8ca1ad36e1edb189b9aed558704ba7bacae0ad592d94f6200f6919980"]}],"invalid_events":[],"applied_event_ids":["sha256:c94fe99f198b32e7ae9fc61da7e0eba20f1b4da1059645aecf6f162985497ef2","sha256:234a2628e7649b5ecb30d6a16728658f9486478216b452070884e2d468bbd83a"],"state_sha256":"0475eeb2b47e125aa91ddfce7ea5eb2ac4f17f4e8d7528f72b91b40b374622e8"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Ko0/2PbsZO8KY7lTLStbXHKbTnQg2tHRdDlTLymVvCnUv9A0oMCuBjUk/rU0qEiNX7iYp18yrbW5AgCGH4DnDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-22T11:07:43.153568Z","bundle_sha256":"574de52fab03d1f0e10e9d70f8f5edf1ffe46d421c51fa97477d0be60b0a8464"}}