{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:2ZMD35UADOZILAHVBWQYVWWT37","short_pith_number":"pith:2ZMD35UA","canonical_record":{"source":{"id":"1103.0519","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-03-02T19:19:51Z","cross_cats_sorted":[],"title_canon_sha256":"74b27efbf5c73af0d1eac2c49d9b1fbf4b63d87cb78548eb63ed22d5d12963ea","abstract_canon_sha256":"cb7aec727757e64743e4f7a23ff167beee8d61a2873a4c387cd30d2f8a064cd0"},"schema_version":"1.0"},"canonical_sha256":"d6583df6801bb28580f50da18adad3dfdf024d7989b2962ca982c394027ede4c","source":{"kind":"arxiv","id":"1103.0519","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1103.0519","created_at":"2026-05-18T04:22:31Z"},{"alias_kind":"arxiv_version","alias_value":"1103.0519v2","created_at":"2026-05-18T04:22:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1103.0519","created_at":"2026-05-18T04:22:31Z"},{"alias_kind":"pith_short_12","alias_value":"2ZMD35UADOZI","created_at":"2026-05-18T12:26:18Z"},{"alias_kind":"pith_short_16","alias_value":"2ZMD35UADOZILAHV","created_at":"2026-05-18T12:26:18Z"},{"alias_kind":"pith_short_8","alias_value":"2ZMD35UA","created_at":"2026-05-18T12:26:18Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:2ZMD35UADOZILAHVBWQYVWWT37","target":"record","payload":{"canonical_record":{"source":{"id":"1103.0519","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-03-02T19:19:51Z","cross_cats_sorted":[],"title_canon_sha256":"74b27efbf5c73af0d1eac2c49d9b1fbf4b63d87cb78548eb63ed22d5d12963ea","abstract_canon_sha256":"cb7aec727757e64743e4f7a23ff167beee8d61a2873a4c387cd30d2f8a064cd0"},"schema_version":"1.0"},"canonical_sha256":"d6583df6801bb28580f50da18adad3dfdf024d7989b2962ca982c394027ede4c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:22:31.721260Z","signature_b64":"AA+5vT7NGXtAZRycmfivR4yZBeM0ymwOMQQwBhnTo8bEGaocORAvJZewagL+vszMtyd7nR3Ng85Vu1KNHJVsAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d6583df6801bb28580f50da18adad3dfdf024d7989b2962ca982c394027ede4c","last_reissued_at":"2026-05-18T04:22:31.720835Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:22:31.720835Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1103.0519","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":"2026-05-18T04:22:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"AxnmoE16NQcUchdcPEQsX4BHzjtPvVoZbVt2XwE4o5mLLT6QxWkriM2uOJ7PO5ajYskKRi4B0YVRxz/8F2n3BQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T00:24:05.902211Z"},"content_sha256":"4bdb1dfe84dd5d8326eab66383f89c82bc5578326c9f4aed0abc7a85dd20781a","schema_version":"1.0","event_id":"sha256:4bdb1dfe84dd5d8326eab66383f89c82bc5578326c9f4aed0abc7a85dd20781a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:2ZMD35UADOZILAHVBWQYVWWT37","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Uniqueness of locally symmetric Brownian motion on Laakso spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Benjamin Steinhurst","submitted_at":"2011-03-02T19:19:51Z","abstract_excerpt":"We take the spaces introduced by Laakso in 2000 and building on the work of Barlow, Bass, Kumagai, and Teplyaev prove the existence and uniqueness of a local symmetry invariant diffusion via heat kernel estimates. This work also builds upon works of Cheeger, Barlow and Bass, as well as the author."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1103.0519","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":"2026-05-18T04:22:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DcPeeAnu0nST3KeFi7vmrhR91JQ5LycZDZndL7im+PpOm/+Z4LiRBSAIYKWltpodYLnm9w/tKBQo8Y/qZpTVCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T00:24:05.902563Z"},"content_sha256":"573909d689b6160974545e4e5a6990ffed3f3ce5f0cb93c7e1f71c2785801a99","schema_version":"1.0","event_id":"sha256:573909d689b6160974545e4e5a6990ffed3f3ce5f0cb93c7e1f71c2785801a99"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/2ZMD35UADOZILAHVBWQYVWWT37/bundle.json","state_url":"https://pith.science/pith/2ZMD35UADOZILAHVBWQYVWWT37/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/2ZMD35UADOZILAHVBWQYVWWT37/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":"2026-06-09T00:24:05Z","links":{"resolver":"https://pith.science/pith/2ZMD35UADOZILAHVBWQYVWWT37","bundle":"https://pith.science/pith/2ZMD35UADOZILAHVBWQYVWWT37/bundle.json","state":"https://pith.science/pith/2ZMD35UADOZILAHVBWQYVWWT37/state.json","well_known_bundle":"https://pith.science/.well-known/pith/2ZMD35UADOZILAHVBWQYVWWT37/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:2ZMD35UADOZILAHVBWQYVWWT37","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":"cb7aec727757e64743e4f7a23ff167beee8d61a2873a4c387cd30d2f8a064cd0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-03-02T19:19:51Z","title_canon_sha256":"74b27efbf5c73af0d1eac2c49d9b1fbf4b63d87cb78548eb63ed22d5d12963ea"},"schema_version":"1.0","source":{"id":"1103.0519","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1103.0519","created_at":"2026-05-18T04:22:31Z"},{"alias_kind":"arxiv_version","alias_value":"1103.0519v2","created_at":"2026-05-18T04:22:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1103.0519","created_at":"2026-05-18T04:22:31Z"},{"alias_kind":"pith_short_12","alias_value":"2ZMD35UADOZI","created_at":"2026-05-18T12:26:18Z"},{"alias_kind":"pith_short_16","alias_value":"2ZMD35UADOZILAHV","created_at":"2026-05-18T12:26:18Z"},{"alias_kind":"pith_short_8","alias_value":"2ZMD35UA","created_at":"2026-05-18T12:26:18Z"}],"graph_snapshots":[{"event_id":"sha256:573909d689b6160974545e4e5a6990ffed3f3ce5f0cb93c7e1f71c2785801a99","target":"graph","created_at":"2026-05-18T04:22:31Z","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":"We take the spaces introduced by Laakso in 2000 and building on the work of Barlow, Bass, Kumagai, and Teplyaev prove the existence and uniqueness of a local symmetry invariant diffusion via heat kernel estimates. This work also builds upon works of Cheeger, Barlow and Bass, as well as the author.","authors_text":"Benjamin Steinhurst","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-03-02T19:19:51Z","title":"Uniqueness of locally symmetric Brownian motion on Laakso spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1103.0519","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":"sha256:4bdb1dfe84dd5d8326eab66383f89c82bc5578326c9f4aed0abc7a85dd20781a","target":"record","created_at":"2026-05-18T04:22:31Z","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":"cb7aec727757e64743e4f7a23ff167beee8d61a2873a4c387cd30d2f8a064cd0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-03-02T19:19:51Z","title_canon_sha256":"74b27efbf5c73af0d1eac2c49d9b1fbf4b63d87cb78548eb63ed22d5d12963ea"},"schema_version":"1.0","source":{"id":"1103.0519","kind":"arxiv","version":2}},"canonical_sha256":"d6583df6801bb28580f50da18adad3dfdf024d7989b2962ca982c394027ede4c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d6583df6801bb28580f50da18adad3dfdf024d7989b2962ca982c394027ede4c","first_computed_at":"2026-05-18T04:22:31.720835Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:22:31.720835Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"AA+5vT7NGXtAZRycmfivR4yZBeM0ymwOMQQwBhnTo8bEGaocORAvJZewagL+vszMtyd7nR3Ng85Vu1KNHJVsAA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:22:31.721260Z","signed_message":"canonical_sha256_bytes"},"source_id":"1103.0519","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4bdb1dfe84dd5d8326eab66383f89c82bc5578326c9f4aed0abc7a85dd20781a","sha256:573909d689b6160974545e4e5a6990ffed3f3ce5f0cb93c7e1f71c2785801a99"],"state_sha256":"a9ebc44272b506f33fc2aee798a7598aa3abc589cbe9cc20a527f5e656da0aca"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"n2O4aITXxnDFkg38V9kwttcfkeYOluJtSLxcw8JxOAM2Y7YkVG9HtroqcesEkIMG/90NSZnegJy6kp1rKtmqAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T00:24:05.904422Z","bundle_sha256":"106f7d51adc915c5e4a3bfbf7b3bcfa7fc9f16a0397de413b35ed54bf990927d"}}