{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2009:QNIN7CQQN3CK7A6SVLX5WXTQSS","short_pith_number":"pith:QNIN7CQQ","canonical_record":{"source":{"id":"0905.3959","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2009-05-25T07:06:17Z","cross_cats_sorted":["math.ST","stat.TH"],"title_canon_sha256":"b3e018ba96dc967de43da3620a8bd07c97695d0a7754ceeb601803cd9a70f15c","abstract_canon_sha256":"65a650499e3400d73e32d590e259ec3b97b7e57d8704faf89173cc3eaf90ee1c"},"schema_version":"1.0"},"canonical_sha256":"8350df8a106ec4af83d2aaefdb5e709492d53a30e3cf10c2837f25e04aa91c0a","source":{"kind":"arxiv","id":"0905.3959","version":5},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0905.3959","created_at":"2026-05-18T02:59:45Z"},{"alias_kind":"arxiv_version","alias_value":"0905.3959v5","created_at":"2026-05-18T02:59:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0905.3959","created_at":"2026-05-18T02:59:45Z"},{"alias_kind":"pith_short_12","alias_value":"QNIN7CQQN3CK","created_at":"2026-05-18T12:26:01Z"},{"alias_kind":"pith_short_16","alias_value":"QNIN7CQQN3CK7A6S","created_at":"2026-05-18T12:26:01Z"},{"alias_kind":"pith_short_8","alias_value":"QNIN7CQQ","created_at":"2026-05-18T12:26:01Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2009:QNIN7CQQN3CK7A6SVLX5WXTQSS","target":"record","payload":{"canonical_record":{"source":{"id":"0905.3959","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2009-05-25T07:06:17Z","cross_cats_sorted":["math.ST","stat.TH"],"title_canon_sha256":"b3e018ba96dc967de43da3620a8bd07c97695d0a7754ceeb601803cd9a70f15c","abstract_canon_sha256":"65a650499e3400d73e32d590e259ec3b97b7e57d8704faf89173cc3eaf90ee1c"},"schema_version":"1.0"},"canonical_sha256":"8350df8a106ec4af83d2aaefdb5e709492d53a30e3cf10c2837f25e04aa91c0a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:59:45.711841Z","signature_b64":"T6gGK+SfRVPVGvGon7W+NGihJv2YZZWrWZH4LGIB6bX8IIyzGBiD8DuY2Vg70rVCbtzMM5b0WuVpB5qoCvLMCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8350df8a106ec4af83d2aaefdb5e709492d53a30e3cf10c2837f25e04aa91c0a","last_reissued_at":"2026-05-18T02:59:45.710952Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:59:45.710952Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0905.3959","source_version":5,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:59:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hZWvuCjt9RXtB+qBxjBs5cqIFtE+W1s6xl6LC9Ztv+btmIeMiKhwAGML9xqToZEP7V+xpF7AHzFTr0C1ZyhwBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T16:35:23.902848Z"},"content_sha256":"ff93e89b5526c9024a51d1b33793d980d621bd7b19a48d0c5f12bd81cded62a5","schema_version":"1.0","event_id":"sha256:ff93e89b5526c9024a51d1b33793d980d621bd7b19a48d0c5f12bd81cded62a5"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2009:QNIN7CQQN3CK7A6SVLX5WXTQSS","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Characterization of Discrete Time Scale Invariant Markov Sequences","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.ST","stat.TH"],"primary_cat":"math.PR","authors_text":"N. Modarresi, S. Rezakhah","submitted_at":"2009-05-25T07:06:17Z","abstract_excerpt":"By considering special sampling of discrete scale invariant (DSI) processes we provide a sequence which is in correspondence to multi-dimensional self-similar process. By imposing Markov property we show that the covariance functions of such discrete scale invariant Markov (DSIM) sequences are characterized by variance, and covariance of adjacent samples in the first scale interval. We also provide a theoretical method for estimating spectral density matrix of corresponding multi-dimensional self-similar Markov process. Some examples such as simple Brownian motion with drift and scale invarian"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0905.3959","kind":"arxiv","version":5},"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":"2026-05-18T02:59:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7Q7kMn6ryTx2Y1ZQt9kXi9eGWdO2J98sxITeBh8APKHDHSKW8GL7Pk+wkRvVCgeoYAUjEz1M5z7YXUAu/M/qBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T16:35:23.903188Z"},"content_sha256":"54155f638e6d84ee69304421f3e16870ba3ef169d18d5950a585476811cd838c","schema_version":"1.0","event_id":"sha256:54155f638e6d84ee69304421f3e16870ba3ef169d18d5950a585476811cd838c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QNIN7CQQN3CK7A6SVLX5WXTQSS/bundle.json","state_url":"https://pith.science/pith/QNIN7CQQN3CK7A6SVLX5WXTQSS/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QNIN7CQQN3CK7A6SVLX5WXTQSS/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":"2026-06-27T16:35:23Z","links":{"resolver":"https://pith.science/pith/QNIN7CQQN3CK7A6SVLX5WXTQSS","bundle":"https://pith.science/pith/QNIN7CQQN3CK7A6SVLX5WXTQSS/bundle.json","state":"https://pith.science/pith/QNIN7CQQN3CK7A6SVLX5WXTQSS/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QNIN7CQQN3CK7A6SVLX5WXTQSS/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:QNIN7CQQN3CK7A6SVLX5WXTQSS","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":"65a650499e3400d73e32d590e259ec3b97b7e57d8704faf89173cc3eaf90ee1c","cross_cats_sorted":["math.ST","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2009-05-25T07:06:17Z","title_canon_sha256":"b3e018ba96dc967de43da3620a8bd07c97695d0a7754ceeb601803cd9a70f15c"},"schema_version":"1.0","source":{"id":"0905.3959","kind":"arxiv","version":5}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0905.3959","created_at":"2026-05-18T02:59:45Z"},{"alias_kind":"arxiv_version","alias_value":"0905.3959v5","created_at":"2026-05-18T02:59:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0905.3959","created_at":"2026-05-18T02:59:45Z"},{"alias_kind":"pith_short_12","alias_value":"QNIN7CQQN3CK","created_at":"2026-05-18T12:26:01Z"},{"alias_kind":"pith_short_16","alias_value":"QNIN7CQQN3CK7A6S","created_at":"2026-05-18T12:26:01Z"},{"alias_kind":"pith_short_8","alias_value":"QNIN7CQQ","created_at":"2026-05-18T12:26:01Z"}],"graph_snapshots":[{"event_id":"sha256:54155f638e6d84ee69304421f3e16870ba3ef169d18d5950a585476811cd838c","target":"graph","created_at":"2026-05-18T02:59:45Z","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":"By considering special sampling of discrete scale invariant (DSI) processes we provide a sequence which is in correspondence to multi-dimensional self-similar process. By imposing Markov property we show that the covariance functions of such discrete scale invariant Markov (DSIM) sequences are characterized by variance, and covariance of adjacent samples in the first scale interval. We also provide a theoretical method for estimating spectral density matrix of corresponding multi-dimensional self-similar Markov process. Some examples such as simple Brownian motion with drift and scale invarian","authors_text":"N. Modarresi, S. Rezakhah","cross_cats":["math.ST","stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2009-05-25T07:06:17Z","title":"Characterization of Discrete Time Scale Invariant Markov Sequences"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0905.3959","kind":"arxiv","version":5},"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:ff93e89b5526c9024a51d1b33793d980d621bd7b19a48d0c5f12bd81cded62a5","target":"record","created_at":"2026-05-18T02:59:45Z","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":"65a650499e3400d73e32d590e259ec3b97b7e57d8704faf89173cc3eaf90ee1c","cross_cats_sorted":["math.ST","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2009-05-25T07:06:17Z","title_canon_sha256":"b3e018ba96dc967de43da3620a8bd07c97695d0a7754ceeb601803cd9a70f15c"},"schema_version":"1.0","source":{"id":"0905.3959","kind":"arxiv","version":5}},"canonical_sha256":"8350df8a106ec4af83d2aaefdb5e709492d53a30e3cf10c2837f25e04aa91c0a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8350df8a106ec4af83d2aaefdb5e709492d53a30e3cf10c2837f25e04aa91c0a","first_computed_at":"2026-05-18T02:59:45.710952Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:59:45.710952Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"T6gGK+SfRVPVGvGon7W+NGihJv2YZZWrWZH4LGIB6bX8IIyzGBiD8DuY2Vg70rVCbtzMM5b0WuVpB5qoCvLMCw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:59:45.711841Z","signed_message":"canonical_sha256_bytes"},"source_id":"0905.3959","source_kind":"arxiv","source_version":5}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ff93e89b5526c9024a51d1b33793d980d621bd7b19a48d0c5f12bd81cded62a5","sha256:54155f638e6d84ee69304421f3e16870ba3ef169d18d5950a585476811cd838c"],"state_sha256":"473c12dabd2cedc32fcfe4e1189af6e57e9fd1c9eea7e71b64438db4f8d95d0c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PLQsBCsdIp6Se/iIhVVnq1aZA5pP8Q6jK5Gxw7ew2jfjC6OXYRRCYNeFEqHbnCPtiOuV60hOkOUfT3gupGibDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-27T16:35:23.905022Z","bundle_sha256":"ecf71c583a89e93caa6afcd49b35ffdea2f3743926da3a63c75d550843d80ca2"}}