{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:WZBV3XPJKIHON74NSQ5WFLDGTE","short_pith_number":"pith:WZBV3XPJ","canonical_record":{"source":{"id":"2505.00277","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2025-05-01T03:57:55Z","cross_cats_sorted":[],"title_canon_sha256":"2af6baf54d613e2c01be9b5662521e798bbc37ea934e01f50101e9482611bbd1","abstract_canon_sha256":"48ab8b368bf46dc8af1533071b006b94e7d4ac5642fda0a3e64e35f6bc4786cf"},"schema_version":"1.0"},"canonical_sha256":"b6435ddde9520ee6ff8d943b62ac66990609fd4cf24e1b3e5c5a4122cdf24a56","source":{"kind":"arxiv","id":"2505.00277","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2505.00277","created_at":"2026-07-05T10:57:10Z"},{"alias_kind":"arxiv_version","alias_value":"2505.00277v1","created_at":"2026-07-05T10:57:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2505.00277","created_at":"2026-07-05T10:57:10Z"},{"alias_kind":"pith_short_12","alias_value":"WZBV3XPJKIHO","created_at":"2026-07-05T10:57:10Z"},{"alias_kind":"pith_short_16","alias_value":"WZBV3XPJKIHON74N","created_at":"2026-07-05T10:57:10Z"},{"alias_kind":"pith_short_8","alias_value":"WZBV3XPJ","created_at":"2026-07-05T10:57:10Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:WZBV3XPJKIHON74NSQ5WFLDGTE","target":"record","payload":{"canonical_record":{"source":{"id":"2505.00277","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2025-05-01T03:57:55Z","cross_cats_sorted":[],"title_canon_sha256":"2af6baf54d613e2c01be9b5662521e798bbc37ea934e01f50101e9482611bbd1","abstract_canon_sha256":"48ab8b368bf46dc8af1533071b006b94e7d4ac5642fda0a3e64e35f6bc4786cf"},"schema_version":"1.0"},"canonical_sha256":"b6435ddde9520ee6ff8d943b62ac66990609fd4cf24e1b3e5c5a4122cdf24a56","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:57:10.886764Z","signature_b64":"RWri+pnn5+dYOqG4lNf2MbRFkMydXgW4X/iahB5y6Bg1KARbqYlUWR5vWAeY3NCoRuQGUGChL7y6l0ThTCA5Bg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b6435ddde9520ee6ff8d943b62ac66990609fd4cf24e1b3e5c5a4122cdf24a56","last_reissued_at":"2026-07-05T10:57:10.886251Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:57:10.886251Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2505.00277","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":"2026-07-05T10:57:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yQwbTYbrYBTm+xLYTlGikIr5xJ5OqDKGH9Pk9JaYxdpDKgI6CYaVVdVPqyI0IMloPLasCWAReaE2c+u2M5pIBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-10T09:55:13.096259Z"},"content_sha256":"28ce3a4fcae455ce4ab48808fa7840e08f600597af9358c1a527f5e452b7d480","schema_version":"1.0","event_id":"sha256:28ce3a4fcae455ce4ab48808fa7840e08f600597af9358c1a527f5e452b7d480"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:WZBV3XPJKIHON74NSQ5WFLDGTE","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Elephant random walk with polynomially decaying steps","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Yuzaburo Nakano","submitted_at":"2025-05-01T03:57:55Z","abstract_excerpt":"In this paper, we introduce a variation of the elephant random walk whose steps are polynomially decaying. At each time $k$, the walker's step size is $k^{-\\gamma}$ with $\\gamma>0$. We investigate effects of the step size exponent $\\gamma$ and the memory parameter $\\alpha\\in [-1,1]$ on the long-time behavior of the walker. For fixed $\\alpha$, it admits phase transition from divergence to convergence (localization) at $\\gamma_{c}(\\alpha)=\\max \\{\\alpha,1/2\\}$. This means that large enough memory effect can shift the critical point for localization. Moreover, we obtain quantitative limit theorems"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.00277","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/2505.00277/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":"2026-07-05T10:57:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WjUGBObCRk29jd6Bo/gIFJ2K6XqY+iO5QmV6P4qGgAN6q4+oXFfzzuxy+9uBlrsp9Van78ooSCgj3mRY1nV3DQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-10T09:55:13.096784Z"},"content_sha256":"a038d714df60d9e70d3490738eb10d1c6aefbe0f7946a1e117074be6c35c0a63","schema_version":"1.0","event_id":"sha256:a038d714df60d9e70d3490738eb10d1c6aefbe0f7946a1e117074be6c35c0a63"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/WZBV3XPJKIHON74NSQ5WFLDGTE/bundle.json","state_url":"https://pith.science/pith/WZBV3XPJKIHON74NSQ5WFLDGTE/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/WZBV3XPJKIHON74NSQ5WFLDGTE/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":"2026-08-10T09:55:13Z","links":{"resolver":"https://pith.science/pith/WZBV3XPJKIHON74NSQ5WFLDGTE","bundle":"https://pith.science/pith/WZBV3XPJKIHON74NSQ5WFLDGTE/bundle.json","state":"https://pith.science/pith/WZBV3XPJKIHON74NSQ5WFLDGTE/state.json","well_known_bundle":"https://pith.science/.well-known/pith/WZBV3XPJKIHON74NSQ5WFLDGTE/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:WZBV3XPJKIHON74NSQ5WFLDGTE","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":"48ab8b368bf46dc8af1533071b006b94e7d4ac5642fda0a3e64e35f6bc4786cf","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2025-05-01T03:57:55Z","title_canon_sha256":"2af6baf54d613e2c01be9b5662521e798bbc37ea934e01f50101e9482611bbd1"},"schema_version":"1.0","source":{"id":"2505.00277","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2505.00277","created_at":"2026-07-05T10:57:10Z"},{"alias_kind":"arxiv_version","alias_value":"2505.00277v1","created_at":"2026-07-05T10:57:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2505.00277","created_at":"2026-07-05T10:57:10Z"},{"alias_kind":"pith_short_12","alias_value":"WZBV3XPJKIHO","created_at":"2026-07-05T10:57:10Z"},{"alias_kind":"pith_short_16","alias_value":"WZBV3XPJKIHON74N","created_at":"2026-07-05T10:57:10Z"},{"alias_kind":"pith_short_8","alias_value":"WZBV3XPJ","created_at":"2026-07-05T10:57:10Z"}],"graph_snapshots":[{"event_id":"sha256:a038d714df60d9e70d3490738eb10d1c6aefbe0f7946a1e117074be6c35c0a63","target":"graph","created_at":"2026-07-05T10:57:10Z","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/2505.00277/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper, we introduce a variation of the elephant random walk whose steps are polynomially decaying. At each time $k$, the walker's step size is $k^{-\\gamma}$ with $\\gamma>0$. We investigate effects of the step size exponent $\\gamma$ and the memory parameter $\\alpha\\in [-1,1]$ on the long-time behavior of the walker. For fixed $\\alpha$, it admits phase transition from divergence to convergence (localization) at $\\gamma_{c}(\\alpha)=\\max \\{\\alpha,1/2\\}$. This means that large enough memory effect can shift the critical point for localization. Moreover, we obtain quantitative limit theorems","authors_text":"Yuzaburo Nakano","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2025-05-01T03:57:55Z","title":"Elephant random walk with polynomially decaying steps"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.00277","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":"sha256:28ce3a4fcae455ce4ab48808fa7840e08f600597af9358c1a527f5e452b7d480","target":"record","created_at":"2026-07-05T10:57:10Z","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":"48ab8b368bf46dc8af1533071b006b94e7d4ac5642fda0a3e64e35f6bc4786cf","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2025-05-01T03:57:55Z","title_canon_sha256":"2af6baf54d613e2c01be9b5662521e798bbc37ea934e01f50101e9482611bbd1"},"schema_version":"1.0","source":{"id":"2505.00277","kind":"arxiv","version":1}},"canonical_sha256":"b6435ddde9520ee6ff8d943b62ac66990609fd4cf24e1b3e5c5a4122cdf24a56","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b6435ddde9520ee6ff8d943b62ac66990609fd4cf24e1b3e5c5a4122cdf24a56","first_computed_at":"2026-07-05T10:57:10.886251Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:57:10.886251Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"RWri+pnn5+dYOqG4lNf2MbRFkMydXgW4X/iahB5y6Bg1KARbqYlUWR5vWAeY3NCoRuQGUGChL7y6l0ThTCA5Bg==","signature_status":"signed_v1","signed_at":"2026-07-05T10:57:10.886764Z","signed_message":"canonical_sha256_bytes"},"source_id":"2505.00277","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:28ce3a4fcae455ce4ab48808fa7840e08f600597af9358c1a527f5e452b7d480","sha256:a038d714df60d9e70d3490738eb10d1c6aefbe0f7946a1e117074be6c35c0a63"],"state_sha256":"685ce464bde5a5b41c3ea12ef6d900930248c37a175afd621c42f59867f987ca"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vqWCdq6Db9kRLTDoiJJg/aqFDj7Zubu1I80k6qfFWeomARnyua+A7kjEhjpKWk7hdbjG9g1LtXyawwVS420AAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-10T09:55:13.101273Z","bundle_sha256":"0aa40c6fd313ebd6f09bff4f3c2e707e31d1076f7540f0278a903779c107f1d6"}}