{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:PGYLY572ZH24QQG57FMIICS2JY","short_pith_number":"pith:PGYLY572","canonical_record":{"source":{"id":"1107.5205","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2011-07-26T13:06:46Z","cross_cats_sorted":[],"title_canon_sha256":"804207519bed20dac3941f8a3714cf96a3bd34167bf60874403e19ac60414d96","abstract_canon_sha256":"fabd36cf0e5dc04a1949a438e8225f7c08c4b473fadfe111723ae9fadb83b446"},"schema_version":"1.0"},"canonical_sha256":"79b0bc77fac9f5c840ddf958840a5a4e339b60aa2792152695c6cce72949ab33","source":{"kind":"arxiv","id":"1107.5205","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1107.5205","created_at":"2026-05-18T04:16:52Z"},{"alias_kind":"arxiv_version","alias_value":"1107.5205v1","created_at":"2026-05-18T04:16:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1107.5205","created_at":"2026-05-18T04:16:52Z"},{"alias_kind":"pith_short_12","alias_value":"PGYLY572ZH24","created_at":"2026-05-18T12:26:39Z"},{"alias_kind":"pith_short_16","alias_value":"PGYLY572ZH24QQG5","created_at":"2026-05-18T12:26:39Z"},{"alias_kind":"pith_short_8","alias_value":"PGYLY572","created_at":"2026-05-18T12:26:39Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:PGYLY572ZH24QQG57FMIICS2JY","target":"record","payload":{"canonical_record":{"source":{"id":"1107.5205","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2011-07-26T13:06:46Z","cross_cats_sorted":[],"title_canon_sha256":"804207519bed20dac3941f8a3714cf96a3bd34167bf60874403e19ac60414d96","abstract_canon_sha256":"fabd36cf0e5dc04a1949a438e8225f7c08c4b473fadfe111723ae9fadb83b446"},"schema_version":"1.0"},"canonical_sha256":"79b0bc77fac9f5c840ddf958840a5a4e339b60aa2792152695c6cce72949ab33","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:16:52.751363Z","signature_b64":"eW8qypweqBOWwl6KQxBfkdID57qXTPyI6W/3pICISgi0qgQiP1JT3m4E8naAIQuCkB9dDLutPy+I9aPUQU2AAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"79b0bc77fac9f5c840ddf958840a5a4e339b60aa2792152695c6cce72949ab33","last_reissued_at":"2026-05-18T04:16:52.750936Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:16:52.750936Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1107.5205","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":"2026-05-18T04:16:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0F52YXVndxkWXfYHmXLXENm3MvvAfOoSSdbYKewzF3Bn5yzzL4ce1z0mW8zUvz7+7uuNA7rIjOVnvlcFd/4TAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T01:14:34.351595Z"},"content_sha256":"24ff50ad8d63ea46a3d8967bfe8e60d8ac0bdf953f71fc5e2a4fd92cea08b655","schema_version":"1.0","event_id":"sha256:24ff50ad8d63ea46a3d8967bfe8e60d8ac0bdf953f71fc5e2a4fd92cea08b655"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:PGYLY572ZH24QQG57FMIICS2JY","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Arveson dichotomy and essential fractality","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OA","authors_text":"Steffen Roch","submitted_at":"2011-07-26T13:06:46Z","abstract_excerpt":"The notions of fractal and essentially fractal algebras of approximation sequences and of the Arveson dichotomy have proved extremely useful for several spectral approximation problems. The purpose of this short note is threefold: to present a short new proof of the fractal restriction theorem, to relate essential fractality with Arveson dichotomy, and to derive a restriction theorem for essential fractality."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1107.5205","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":"2026-05-18T04:16:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dOeZ/T8bHltL5zvdXBsDdTiAak38DgrGTwHOOxgrlnV1AKGTJlTwKqKULlkdowXyLBgu50Hyq1pufjxxj30QAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T01:14:34.352187Z"},"content_sha256":"f4bd78981f9b8177a64baac0d5cc16d4554567e0ca76c5ab73c7c9a808699fc2","schema_version":"1.0","event_id":"sha256:f4bd78981f9b8177a64baac0d5cc16d4554567e0ca76c5ab73c7c9a808699fc2"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/PGYLY572ZH24QQG57FMIICS2JY/bundle.json","state_url":"https://pith.science/pith/PGYLY572ZH24QQG57FMIICS2JY/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/PGYLY572ZH24QQG57FMIICS2JY/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":"2026-06-01T01:14:34Z","links":{"resolver":"https://pith.science/pith/PGYLY572ZH24QQG57FMIICS2JY","bundle":"https://pith.science/pith/PGYLY572ZH24QQG57FMIICS2JY/bundle.json","state":"https://pith.science/pith/PGYLY572ZH24QQG57FMIICS2JY/state.json","well_known_bundle":"https://pith.science/.well-known/pith/PGYLY572ZH24QQG57FMIICS2JY/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:PGYLY572ZH24QQG57FMIICS2JY","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":"fabd36cf0e5dc04a1949a438e8225f7c08c4b473fadfe111723ae9fadb83b446","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2011-07-26T13:06:46Z","title_canon_sha256":"804207519bed20dac3941f8a3714cf96a3bd34167bf60874403e19ac60414d96"},"schema_version":"1.0","source":{"id":"1107.5205","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1107.5205","created_at":"2026-05-18T04:16:52Z"},{"alias_kind":"arxiv_version","alias_value":"1107.5205v1","created_at":"2026-05-18T04:16:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1107.5205","created_at":"2026-05-18T04:16:52Z"},{"alias_kind":"pith_short_12","alias_value":"PGYLY572ZH24","created_at":"2026-05-18T12:26:39Z"},{"alias_kind":"pith_short_16","alias_value":"PGYLY572ZH24QQG5","created_at":"2026-05-18T12:26:39Z"},{"alias_kind":"pith_short_8","alias_value":"PGYLY572","created_at":"2026-05-18T12:26:39Z"}],"graph_snapshots":[{"event_id":"sha256:f4bd78981f9b8177a64baac0d5cc16d4554567e0ca76c5ab73c7c9a808699fc2","target":"graph","created_at":"2026-05-18T04:16:52Z","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":"The notions of fractal and essentially fractal algebras of approximation sequences and of the Arveson dichotomy have proved extremely useful for several spectral approximation problems. The purpose of this short note is threefold: to present a short new proof of the fractal restriction theorem, to relate essential fractality with Arveson dichotomy, and to derive a restriction theorem for essential fractality.","authors_text":"Steffen Roch","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2011-07-26T13:06:46Z","title":"Arveson dichotomy and essential fractality"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1107.5205","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":"sha256:24ff50ad8d63ea46a3d8967bfe8e60d8ac0bdf953f71fc5e2a4fd92cea08b655","target":"record","created_at":"2026-05-18T04:16:52Z","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":"fabd36cf0e5dc04a1949a438e8225f7c08c4b473fadfe111723ae9fadb83b446","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2011-07-26T13:06:46Z","title_canon_sha256":"804207519bed20dac3941f8a3714cf96a3bd34167bf60874403e19ac60414d96"},"schema_version":"1.0","source":{"id":"1107.5205","kind":"arxiv","version":1}},"canonical_sha256":"79b0bc77fac9f5c840ddf958840a5a4e339b60aa2792152695c6cce72949ab33","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"79b0bc77fac9f5c840ddf958840a5a4e339b60aa2792152695c6cce72949ab33","first_computed_at":"2026-05-18T04:16:52.750936Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:16:52.750936Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"eW8qypweqBOWwl6KQxBfkdID57qXTPyI6W/3pICISgi0qgQiP1JT3m4E8naAIQuCkB9dDLutPy+I9aPUQU2AAg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:16:52.751363Z","signed_message":"canonical_sha256_bytes"},"source_id":"1107.5205","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:24ff50ad8d63ea46a3d8967bfe8e60d8ac0bdf953f71fc5e2a4fd92cea08b655","sha256:f4bd78981f9b8177a64baac0d5cc16d4554567e0ca76c5ab73c7c9a808699fc2"],"state_sha256":"70438dfdf899859f1a0931e00cf2f49d79195ef3117dd341af06b7c52aec15fd"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"aE0TKrJx3mOSoTreH0ZNc/nvhHfV3T8TF+A65Bk+dpCioNSMveqyvE+vm7Xhh9lDZ6vy8+fjCz+hbEED39VlBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T01:14:34.355589Z","bundle_sha256":"a1cf1c4a94289388c9b7f140d81adde78f64d610414d274ae1e5bd52171a3060"}}