{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:GXNAMBM2LTFIISNXOWHJLGUPYS","short_pith_number":"pith:GXNAMBM2","canonical_record":{"source":{"id":"1704.06850","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2017-04-22T21:02:31Z","cross_cats_sorted":["cs.DS"],"title_canon_sha256":"e31f9e558075aa9e4f36dc5fcc74847237e6e29f271099b9193edea9df435ef1","abstract_canon_sha256":"b6123734bf5ea7206c046d4484dc5359e7a30c8ee34e74818da8192371adc34e"},"schema_version":"1.0"},"canonical_sha256":"35da06059a5cca8449b7758e959a8fc4a798305657c98b84f6272cd1d5bf1c25","source":{"kind":"arxiv","id":"1704.06850","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1704.06850","created_at":"2026-05-18T00:29:01Z"},{"alias_kind":"arxiv_version","alias_value":"1704.06850v2","created_at":"2026-05-18T00:29:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1704.06850","created_at":"2026-05-18T00:29:01Z"},{"alias_kind":"pith_short_12","alias_value":"GXNAMBM2LTFI","created_at":"2026-05-18T12:31:18Z"},{"alias_kind":"pith_short_16","alias_value":"GXNAMBM2LTFIISNX","created_at":"2026-05-18T12:31:18Z"},{"alias_kind":"pith_short_8","alias_value":"GXNAMBM2","created_at":"2026-05-18T12:31:18Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:GXNAMBM2LTFIISNXOWHJLGUPYS","target":"record","payload":{"canonical_record":{"source":{"id":"1704.06850","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2017-04-22T21:02:31Z","cross_cats_sorted":["cs.DS"],"title_canon_sha256":"e31f9e558075aa9e4f36dc5fcc74847237e6e29f271099b9193edea9df435ef1","abstract_canon_sha256":"b6123734bf5ea7206c046d4484dc5359e7a30c8ee34e74818da8192371adc34e"},"schema_version":"1.0"},"canonical_sha256":"35da06059a5cca8449b7758e959a8fc4a798305657c98b84f6272cd1d5bf1c25","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:29:01.533029Z","signature_b64":"rZF9BwAqCvH7eNucd43JtlGAdjPUaIZ5j5ojPB1I8OGYSFUjwi3ll9OD1RL6XR0u0dGZtJLg1oFYd/OPBNDoDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"35da06059a5cca8449b7758e959a8fc4a798305657c98b84f6272cd1d5bf1c25","last_reissued_at":"2026-05-18T00:29:01.532578Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:29:01.532578Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1704.06850","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":"2026-05-18T00:29:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QleNUvkydHpzNoxwt/LEuJ+kxRRwT0Hjtn3tg+Erk9Ni/bYT1U6t+QK5mT57UV/tWASI6ZTN0M5Wn+JcZuVJDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T17:55:06.078897Z"},"content_sha256":"e1bbbcb0c60dbd78acdcc2821ed21af7f8cf8893fd1de3990d5e0f73fae9950f","schema_version":"1.0","event_id":"sha256:e1bbbcb0c60dbd78acdcc2821ed21af7f8cf8893fd1de3990d5e0f73fae9950f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:GXNAMBM2LTFIISNXOWHJLGUPYS","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Testing Symmetric Markov Chains from a Single Trajectory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DS"],"primary_cat":"cs.LG","authors_text":"Constantinos Daskalakis, Nick Gravin, Nishanth Dikkala","submitted_at":"2017-04-22T21:02:31Z","abstract_excerpt":"Classical distribution testing assumes access to i.i.d. samples from the distribution that is being tested. We initiate the study of Markov chain testing, assuming access to a single trajectory of a Markov Chain. In particular, we observe a single trajectory X0,...,Xt,... of an unknown, symmetric, and finite state Markov Chain M. We do not control the starting state X0, and we cannot restart the chain. Given our single trajectory, the goal is to test whether M is identical to a model Markov Chain M0 , or far from it under an appropriate notion of difference. We propose a measure of difference "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.06850","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":""},"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":"2026-05-18T00:29:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BFwHR0JHu+1Wzz21PdsD4uudp/6ror+/zZBTyDGqtDTc4Z2W/i5JjXUAHoNVhkHIBARISi9z31zABmomCbsgDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T17:55:06.079240Z"},"content_sha256":"c7b52f2d2558dabaa0465eadef1ca2204122f08e580c9b5f77c195f6107ae079","schema_version":"1.0","event_id":"sha256:c7b52f2d2558dabaa0465eadef1ca2204122f08e580c9b5f77c195f6107ae079"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GXNAMBM2LTFIISNXOWHJLGUPYS/bundle.json","state_url":"https://pith.science/pith/GXNAMBM2LTFIISNXOWHJLGUPYS/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GXNAMBM2LTFIISNXOWHJLGUPYS/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":"2026-06-02T17:55:06Z","links":{"resolver":"https://pith.science/pith/GXNAMBM2LTFIISNXOWHJLGUPYS","bundle":"https://pith.science/pith/GXNAMBM2LTFIISNXOWHJLGUPYS/bundle.json","state":"https://pith.science/pith/GXNAMBM2LTFIISNXOWHJLGUPYS/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GXNAMBM2LTFIISNXOWHJLGUPYS/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:GXNAMBM2LTFIISNXOWHJLGUPYS","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":"b6123734bf5ea7206c046d4484dc5359e7a30c8ee34e74818da8192371adc34e","cross_cats_sorted":["cs.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2017-04-22T21:02:31Z","title_canon_sha256":"e31f9e558075aa9e4f36dc5fcc74847237e6e29f271099b9193edea9df435ef1"},"schema_version":"1.0","source":{"id":"1704.06850","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1704.06850","created_at":"2026-05-18T00:29:01Z"},{"alias_kind":"arxiv_version","alias_value":"1704.06850v2","created_at":"2026-05-18T00:29:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1704.06850","created_at":"2026-05-18T00:29:01Z"},{"alias_kind":"pith_short_12","alias_value":"GXNAMBM2LTFI","created_at":"2026-05-18T12:31:18Z"},{"alias_kind":"pith_short_16","alias_value":"GXNAMBM2LTFIISNX","created_at":"2026-05-18T12:31:18Z"},{"alias_kind":"pith_short_8","alias_value":"GXNAMBM2","created_at":"2026-05-18T12:31:18Z"}],"graph_snapshots":[{"event_id":"sha256:c7b52f2d2558dabaa0465eadef1ca2204122f08e580c9b5f77c195f6107ae079","target":"graph","created_at":"2026-05-18T00:29:01Z","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":"Classical distribution testing assumes access to i.i.d. samples from the distribution that is being tested. We initiate the study of Markov chain testing, assuming access to a single trajectory of a Markov Chain. In particular, we observe a single trajectory X0,...,Xt,... of an unknown, symmetric, and finite state Markov Chain M. We do not control the starting state X0, and we cannot restart the chain. Given our single trajectory, the goal is to test whether M is identical to a model Markov Chain M0 , or far from it under an appropriate notion of difference. We propose a measure of difference ","authors_text":"Constantinos Daskalakis, Nick Gravin, Nishanth Dikkala","cross_cats":["cs.DS"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2017-04-22T21:02:31Z","title":"Testing Symmetric Markov Chains from a Single Trajectory"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.06850","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:e1bbbcb0c60dbd78acdcc2821ed21af7f8cf8893fd1de3990d5e0f73fae9950f","target":"record","created_at":"2026-05-18T00:29:01Z","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":"b6123734bf5ea7206c046d4484dc5359e7a30c8ee34e74818da8192371adc34e","cross_cats_sorted":["cs.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2017-04-22T21:02:31Z","title_canon_sha256":"e31f9e558075aa9e4f36dc5fcc74847237e6e29f271099b9193edea9df435ef1"},"schema_version":"1.0","source":{"id":"1704.06850","kind":"arxiv","version":2}},"canonical_sha256":"35da06059a5cca8449b7758e959a8fc4a798305657c98b84f6272cd1d5bf1c25","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"35da06059a5cca8449b7758e959a8fc4a798305657c98b84f6272cd1d5bf1c25","first_computed_at":"2026-05-18T00:29:01.532578Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:29:01.532578Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"rZF9BwAqCvH7eNucd43JtlGAdjPUaIZ5j5ojPB1I8OGYSFUjwi3ll9OD1RL6XR0u0dGZtJLg1oFYd/OPBNDoDA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:29:01.533029Z","signed_message":"canonical_sha256_bytes"},"source_id":"1704.06850","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e1bbbcb0c60dbd78acdcc2821ed21af7f8cf8893fd1de3990d5e0f73fae9950f","sha256:c7b52f2d2558dabaa0465eadef1ca2204122f08e580c9b5f77c195f6107ae079"],"state_sha256":"983defd37780d556d07fd21e956390e9ad083ac59b8af4fce750db9fbcc4c64e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"R/H9zm5Wlxy3NzKt1V7DR1sgfYqY0luCywho0+7bBNso5f8+aftzR6i0N7V7v9l8Y/kFPLwRO4i9G2HV16jkBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T17:55:06.081569Z","bundle_sha256":"227bb93eb6f71fd1e220562496811b8cf11a88ed7f54c5bde9c40eb45d2dd9d8"}}