{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:PWD4Q2QC7L2PDJRYPUM7P7OVT7","short_pith_number":"pith:PWD4Q2QC","canonical_record":{"source":{"id":"1805.06063","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2018-05-15T23:12:25Z","cross_cats_sorted":["math-ph","math.DS","math.MP","math.OA","math.PR"],"title_canon_sha256":"8563c96f2bb365d6de9dab8e03697328fa7458165fcc9ba7bd34e3320b26d837","abstract_canon_sha256":"376c88ccce2dc03dabc5bf53242e6945e2c7e6d0cad3e6795983e5a8a00fd1d5"},"schema_version":"1.0"},"canonical_sha256":"7d87c86a02faf4f1a6387d19f7fdd59fd7aaec1bf136628df175eb1d66a56c32","source":{"kind":"arxiv","id":"1805.06063","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1805.06063","created_at":"2026-05-18T00:15:49Z"},{"alias_kind":"arxiv_version","alias_value":"1805.06063v1","created_at":"2026-05-18T00:15:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1805.06063","created_at":"2026-05-18T00:15:49Z"},{"alias_kind":"pith_short_12","alias_value":"PWD4Q2QC7L2P","created_at":"2026-05-18T12:32:46Z"},{"alias_kind":"pith_short_16","alias_value":"PWD4Q2QC7L2PDJRY","created_at":"2026-05-18T12:32:46Z"},{"alias_kind":"pith_short_8","alias_value":"PWD4Q2QC","created_at":"2026-05-18T12:32:46Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:PWD4Q2QC7L2PDJRYPUM7P7OVT7","target":"record","payload":{"canonical_record":{"source":{"id":"1805.06063","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2018-05-15T23:12:25Z","cross_cats_sorted":["math-ph","math.DS","math.MP","math.OA","math.PR"],"title_canon_sha256":"8563c96f2bb365d6de9dab8e03697328fa7458165fcc9ba7bd34e3320b26d837","abstract_canon_sha256":"376c88ccce2dc03dabc5bf53242e6945e2c7e6d0cad3e6795983e5a8a00fd1d5"},"schema_version":"1.0"},"canonical_sha256":"7d87c86a02faf4f1a6387d19f7fdd59fd7aaec1bf136628df175eb1d66a56c32","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:15:49.004687Z","signature_b64":"X1yHR9D+Ad1c7z6OaVuyOsjfZn6mD/SxjH/Sq8ZwCi9p6oVVWPeiqj50x33WLH38XOnmXYS6yER/tzHiMXhfDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7d87c86a02faf4f1a6387d19f7fdd59fd7aaec1bf136628df175eb1d66a56c32","last_reissued_at":"2026-05-18T00:15:49.004233Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:15:49.004233Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1805.06063","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":"2026-05-18T00:15:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rBRG3cHnWPzW5SnH0D0/mZbjTry0Y/vAmqHQOoYCpp7uCGmTDe3zlPmYTK4JryiNg2BqTVp0aoW9dRLcj0mtDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T05:53:01.263934Z"},"content_sha256":"1b83c35725768289797bd48b4a1956229a2dfa9a1a115fc6d8a05e61527e8fee","schema_version":"1.0","event_id":"sha256:1b83c35725768289797bd48b4a1956229a2dfa9a1a115fc6d8a05e61527e8fee"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:PWD4Q2QC7L2PDJRYPUM7P7OVT7","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Martin boundaries of representations of the Cuntz algebra","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.DS","math.MP","math.OA","math.PR"],"primary_cat":"math.FA","authors_text":"Feng Tian, Palle Jorgensen","submitted_at":"2018-05-15T23:12:25Z","abstract_excerpt":"In a number of recent papers, the idea of generalized boundaries has found use in fractal and in multiresolution analysis; many of the papers having a focus on specific examples. Parallel with this new insight, and motivated by quantum probability, there has also been much research which seeks to study fractal and multiresolution structures with the use of certain systems of non-commutative operators; non-commutative harmonic/stochastic analysis. This in turn entails combinatorial, graph operations, and branching laws. The most versatile, of these non-commutative algebras are the Cuntz algebra"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.06063","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":""},"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":"2026-05-18T00:15:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uuC44ygGhhSW3b6+R5JMBAxJzKrmRyU3F0cwIfrh7tWGmeG/2zpHRHDgceeXkD2h5smaXmUIkts+Picub5orBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T05:53:01.264699Z"},"content_sha256":"9cd4fd7c4d9ef0baba53e3df68f1969d6f5cd58da45aab271acb908137cccbad","schema_version":"1.0","event_id":"sha256:9cd4fd7c4d9ef0baba53e3df68f1969d6f5cd58da45aab271acb908137cccbad"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/PWD4Q2QC7L2PDJRYPUM7P7OVT7/bundle.json","state_url":"https://pith.science/pith/PWD4Q2QC7L2PDJRYPUM7P7OVT7/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/PWD4Q2QC7L2PDJRYPUM7P7OVT7/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":"2026-05-30T05:53:01Z","links":{"resolver":"https://pith.science/pith/PWD4Q2QC7L2PDJRYPUM7P7OVT7","bundle":"https://pith.science/pith/PWD4Q2QC7L2PDJRYPUM7P7OVT7/bundle.json","state":"https://pith.science/pith/PWD4Q2QC7L2PDJRYPUM7P7OVT7/state.json","well_known_bundle":"https://pith.science/.well-known/pith/PWD4Q2QC7L2PDJRYPUM7P7OVT7/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:PWD4Q2QC7L2PDJRYPUM7P7OVT7","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":"376c88ccce2dc03dabc5bf53242e6945e2c7e6d0cad3e6795983e5a8a00fd1d5","cross_cats_sorted":["math-ph","math.DS","math.MP","math.OA","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2018-05-15T23:12:25Z","title_canon_sha256":"8563c96f2bb365d6de9dab8e03697328fa7458165fcc9ba7bd34e3320b26d837"},"schema_version":"1.0","source":{"id":"1805.06063","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1805.06063","created_at":"2026-05-18T00:15:49Z"},{"alias_kind":"arxiv_version","alias_value":"1805.06063v1","created_at":"2026-05-18T00:15:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1805.06063","created_at":"2026-05-18T00:15:49Z"},{"alias_kind":"pith_short_12","alias_value":"PWD4Q2QC7L2P","created_at":"2026-05-18T12:32:46Z"},{"alias_kind":"pith_short_16","alias_value":"PWD4Q2QC7L2PDJRY","created_at":"2026-05-18T12:32:46Z"},{"alias_kind":"pith_short_8","alias_value":"PWD4Q2QC","created_at":"2026-05-18T12:32:46Z"}],"graph_snapshots":[{"event_id":"sha256:9cd4fd7c4d9ef0baba53e3df68f1969d6f5cd58da45aab271acb908137cccbad","target":"graph","created_at":"2026-05-18T00:15:49Z","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":"In a number of recent papers, the idea of generalized boundaries has found use in fractal and in multiresolution analysis; many of the papers having a focus on specific examples. Parallel with this new insight, and motivated by quantum probability, there has also been much research which seeks to study fractal and multiresolution structures with the use of certain systems of non-commutative operators; non-commutative harmonic/stochastic analysis. This in turn entails combinatorial, graph operations, and branching laws. The most versatile, of these non-commutative algebras are the Cuntz algebra","authors_text":"Feng Tian, Palle Jorgensen","cross_cats":["math-ph","math.DS","math.MP","math.OA","math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2018-05-15T23:12:25Z","title":"Martin boundaries of representations of the Cuntz algebra"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.06063","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":"sha256:1b83c35725768289797bd48b4a1956229a2dfa9a1a115fc6d8a05e61527e8fee","target":"record","created_at":"2026-05-18T00:15:49Z","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":"376c88ccce2dc03dabc5bf53242e6945e2c7e6d0cad3e6795983e5a8a00fd1d5","cross_cats_sorted":["math-ph","math.DS","math.MP","math.OA","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2018-05-15T23:12:25Z","title_canon_sha256":"8563c96f2bb365d6de9dab8e03697328fa7458165fcc9ba7bd34e3320b26d837"},"schema_version":"1.0","source":{"id":"1805.06063","kind":"arxiv","version":1}},"canonical_sha256":"7d87c86a02faf4f1a6387d19f7fdd59fd7aaec1bf136628df175eb1d66a56c32","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7d87c86a02faf4f1a6387d19f7fdd59fd7aaec1bf136628df175eb1d66a56c32","first_computed_at":"2026-05-18T00:15:49.004233Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:15:49.004233Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"X1yHR9D+Ad1c7z6OaVuyOsjfZn6mD/SxjH/Sq8ZwCi9p6oVVWPeiqj50x33WLH38XOnmXYS6yER/tzHiMXhfDg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:15:49.004687Z","signed_message":"canonical_sha256_bytes"},"source_id":"1805.06063","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1b83c35725768289797bd48b4a1956229a2dfa9a1a115fc6d8a05e61527e8fee","sha256:9cd4fd7c4d9ef0baba53e3df68f1969d6f5cd58da45aab271acb908137cccbad"],"state_sha256":"5b7c50cd311bb4e78ed1fb24084109082fc16bcfbe58a6952e062bc5ec5c71ce"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1missszfT1XOxBk02PaXv6NKD0nubPQzFDjze6xRXkbdyGlgFD/uCWy+3NbsUuoQ/T1wBa1w2/C2h7aB0yWSBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T05:53:01.268537Z","bundle_sha256":"39a34cfee7fb28d1165f657745bc8c5f66606fc2db8b31e82b17833e59a6ab17"}}