{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:6TG6PYYGRFX4V42G7TREZJHFRQ","short_pith_number":"pith:6TG6PYYG","canonical_record":{"source":{"id":"1409.8022","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2014-09-29T08:27:17Z","cross_cats_sorted":[],"title_canon_sha256":"ee45c76fdc4e92717032328dec5b997fc06488098ea113832fba2b08d02b66b9","abstract_canon_sha256":"e59308ea646f82a101e12eed5db120ee4f8988c5674489a6c02171e78aeb3923"},"schema_version":"1.0"},"canonical_sha256":"f4cde7e306896fcaf346fce24ca4e58c13beb784cdcf86565b0e93facb900490","source":{"kind":"arxiv","id":"1409.8022","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1409.8022","created_at":"2026-05-18T02:41:33Z"},{"alias_kind":"arxiv_version","alias_value":"1409.8022v1","created_at":"2026-05-18T02:41:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1409.8022","created_at":"2026-05-18T02:41:33Z"},{"alias_kind":"pith_short_12","alias_value":"6TG6PYYGRFX4","created_at":"2026-05-18T12:28:16Z"},{"alias_kind":"pith_short_16","alias_value":"6TG6PYYGRFX4V42G","created_at":"2026-05-18T12:28:16Z"},{"alias_kind":"pith_short_8","alias_value":"6TG6PYYG","created_at":"2026-05-18T12:28:16Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:6TG6PYYGRFX4V42G7TREZJHFRQ","target":"record","payload":{"canonical_record":{"source":{"id":"1409.8022","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2014-09-29T08:27:17Z","cross_cats_sorted":[],"title_canon_sha256":"ee45c76fdc4e92717032328dec5b997fc06488098ea113832fba2b08d02b66b9","abstract_canon_sha256":"e59308ea646f82a101e12eed5db120ee4f8988c5674489a6c02171e78aeb3923"},"schema_version":"1.0"},"canonical_sha256":"f4cde7e306896fcaf346fce24ca4e58c13beb784cdcf86565b0e93facb900490","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:41:33.852206Z","signature_b64":"aQ3jo2KHQERAwcgZwAeSi5GRY2qP6d7rRYFrG+00b0u87F7EL9o/+tEMoEI2ZrU9UMooPh9+bcYF22ECDzxHAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f4cde7e306896fcaf346fce24ca4e58c13beb784cdcf86565b0e93facb900490","last_reissued_at":"2026-05-18T02:41:33.851846Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:41:33.851846Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1409.8022","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":"2026-05-18T02:41:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tJyh6G30w9WlQnj7PC+fbBYSVhZEyzv0c8PbCWh9OIC8Ni+FfGCeYkvH+v0FZF6HJB4Xxb+grqf7cQgzO1DrBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T07:53:32.489059Z"},"content_sha256":"5568f81f48f7c3f0e1620fcd00c978a1349cceffb3d359006a5a0d5fcb946cdb","schema_version":"1.0","event_id":"sha256:5568f81f48f7c3f0e1620fcd00c978a1349cceffb3d359006a5a0d5fcb946cdb"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:6TG6PYYGRFX4V42G7TREZJHFRQ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Subnormal weighted shifts on directed trees whose nth powers have trivial domain","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Il Bong Jung, Jan Stochel, Piotr Budzynski, Zenon Jan Jablonski","submitted_at":"2014-09-29T08:27:17Z","abstract_excerpt":"It is shown that for any positive integer n there exists a subnormal weighted shift on a directed tree whose nth power is closed and densely defined while its (n + 1)th power has trivial domain. Similar result for composition operators in L2-spaces is established."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.8022","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":"2026-05-18T02:41:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JbqyBY6Cmvx8k42yRLs22s545/PKlyWDqBi1T817Rc1buLeLiPqqjF5OY2vmcswu5T1UKBeMpvu6sVfE9c0+AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T07:53:32.489754Z"},"content_sha256":"2ce2976516f98feb5c32348d2169e4da2cd0cb1cc7f85b1e9a9ed4f47a6443fb","schema_version":"1.0","event_id":"sha256:2ce2976516f98feb5c32348d2169e4da2cd0cb1cc7f85b1e9a9ed4f47a6443fb"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6TG6PYYGRFX4V42G7TREZJHFRQ/bundle.json","state_url":"https://pith.science/pith/6TG6PYYGRFX4V42G7TREZJHFRQ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6TG6PYYGRFX4V42G7TREZJHFRQ/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":"2026-06-11T07:53:32Z","links":{"resolver":"https://pith.science/pith/6TG6PYYGRFX4V42G7TREZJHFRQ","bundle":"https://pith.science/pith/6TG6PYYGRFX4V42G7TREZJHFRQ/bundle.json","state":"https://pith.science/pith/6TG6PYYGRFX4V42G7TREZJHFRQ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6TG6PYYGRFX4V42G7TREZJHFRQ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:6TG6PYYGRFX4V42G7TREZJHFRQ","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":"e59308ea646f82a101e12eed5db120ee4f8988c5674489a6c02171e78aeb3923","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2014-09-29T08:27:17Z","title_canon_sha256":"ee45c76fdc4e92717032328dec5b997fc06488098ea113832fba2b08d02b66b9"},"schema_version":"1.0","source":{"id":"1409.8022","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1409.8022","created_at":"2026-05-18T02:41:33Z"},{"alias_kind":"arxiv_version","alias_value":"1409.8022v1","created_at":"2026-05-18T02:41:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1409.8022","created_at":"2026-05-18T02:41:33Z"},{"alias_kind":"pith_short_12","alias_value":"6TG6PYYGRFX4","created_at":"2026-05-18T12:28:16Z"},{"alias_kind":"pith_short_16","alias_value":"6TG6PYYGRFX4V42G","created_at":"2026-05-18T12:28:16Z"},{"alias_kind":"pith_short_8","alias_value":"6TG6PYYG","created_at":"2026-05-18T12:28:16Z"}],"graph_snapshots":[{"event_id":"sha256:2ce2976516f98feb5c32348d2169e4da2cd0cb1cc7f85b1e9a9ed4f47a6443fb","target":"graph","created_at":"2026-05-18T02:41:33Z","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":"It is shown that for any positive integer n there exists a subnormal weighted shift on a directed tree whose nth power is closed and densely defined while its (n + 1)th power has trivial domain. Similar result for composition operators in L2-spaces is established.","authors_text":"Il Bong Jung, Jan Stochel, Piotr Budzynski, Zenon Jan Jablonski","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2014-09-29T08:27:17Z","title":"Subnormal weighted shifts on directed trees whose nth powers have trivial domain"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.8022","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":"sha256:5568f81f48f7c3f0e1620fcd00c978a1349cceffb3d359006a5a0d5fcb946cdb","target":"record","created_at":"2026-05-18T02:41:33Z","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":"e59308ea646f82a101e12eed5db120ee4f8988c5674489a6c02171e78aeb3923","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2014-09-29T08:27:17Z","title_canon_sha256":"ee45c76fdc4e92717032328dec5b997fc06488098ea113832fba2b08d02b66b9"},"schema_version":"1.0","source":{"id":"1409.8022","kind":"arxiv","version":1}},"canonical_sha256":"f4cde7e306896fcaf346fce24ca4e58c13beb784cdcf86565b0e93facb900490","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f4cde7e306896fcaf346fce24ca4e58c13beb784cdcf86565b0e93facb900490","first_computed_at":"2026-05-18T02:41:33.851846Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:41:33.851846Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"aQ3jo2KHQERAwcgZwAeSi5GRY2qP6d7rRYFrG+00b0u87F7EL9o/+tEMoEI2ZrU9UMooPh9+bcYF22ECDzxHAg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:41:33.852206Z","signed_message":"canonical_sha256_bytes"},"source_id":"1409.8022","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5568f81f48f7c3f0e1620fcd00c978a1349cceffb3d359006a5a0d5fcb946cdb","sha256:2ce2976516f98feb5c32348d2169e4da2cd0cb1cc7f85b1e9a9ed4f47a6443fb"],"state_sha256":"9e654cd44ec8658254c741ef320605754ee8ea4692b0efd92b41c379fc5ce9fb"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5SHvs8sXGnLLbVRnH4ANB5dga3JnrEi657ErPGkJbEi2pJ/+LR/c8IDqqLKWC+imC1y0T1NoAi/7LzyHb7v0DQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-11T07:53:32.493382Z","bundle_sha256":"e377e715bce7bb5efe4efb65dcc3d60a7c93aa5c8b116b68cff5c57128861f11"}}