{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:QZPUDH4PIG354HQCMICUHRTD3K","short_pith_number":"pith:QZPUDH4P","canonical_record":{"source":{"id":"1207.5835","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2012-07-24T21:42:10Z","cross_cats_sorted":[],"title_canon_sha256":"9b4e2525722739087cafc04fa4fa759be22bddcf924e4cebe082bca3c4e25f3f","abstract_canon_sha256":"77402d57ca30644d89ac05b031eae3ae527f3eabc05a3fc0f015d66f41bc38c8"},"schema_version":"1.0"},"canonical_sha256":"865f419f8f41b7de1e02620543c663da8bd51c3d6762082ef3ecdd0c92032b5c","source":{"kind":"arxiv","id":"1207.5835","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1207.5835","created_at":"2026-05-18T03:20:20Z"},{"alias_kind":"arxiv_version","alias_value":"1207.5835v3","created_at":"2026-05-18T03:20:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1207.5835","created_at":"2026-05-18T03:20:20Z"},{"alias_kind":"pith_short_12","alias_value":"QZPUDH4PIG35","created_at":"2026-05-18T12:27:20Z"},{"alias_kind":"pith_short_16","alias_value":"QZPUDH4PIG354HQC","created_at":"2026-05-18T12:27:20Z"},{"alias_kind":"pith_short_8","alias_value":"QZPUDH4P","created_at":"2026-05-18T12:27:20Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:QZPUDH4PIG354HQCMICUHRTD3K","target":"record","payload":{"canonical_record":{"source":{"id":"1207.5835","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2012-07-24T21:42:10Z","cross_cats_sorted":[],"title_canon_sha256":"9b4e2525722739087cafc04fa4fa759be22bddcf924e4cebe082bca3c4e25f3f","abstract_canon_sha256":"77402d57ca30644d89ac05b031eae3ae527f3eabc05a3fc0f015d66f41bc38c8"},"schema_version":"1.0"},"canonical_sha256":"865f419f8f41b7de1e02620543c663da8bd51c3d6762082ef3ecdd0c92032b5c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:20:20.785070Z","signature_b64":"3z1PBUFJED3mu0PEArINHbqc+Kz6Q2dCvhDUYbtC2OHRrbny/7zMD0LHDLvxH1VGO1EdWCA6dgctUibIUe9yCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"865f419f8f41b7de1e02620543c663da8bd51c3d6762082ef3ecdd0c92032b5c","last_reissued_at":"2026-05-18T03:20:20.784101Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:20:20.784101Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1207.5835","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:20:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DPF7rttotXl/Oj+eJEx+YV225gi/tEQBTG+Gp+Un2tpjDCSKiOWC4smvvscX06I9SyiSIUoYrL32EbDgzk+SDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T09:40:26.861780Z"},"content_sha256":"adafc7256f9326f9b9fe629b3ba2fbb551517663eb6c4050de477633d4226512","schema_version":"1.0","event_id":"sha256:adafc7256f9326f9b9fe629b3ba2fbb551517663eb6c4050de477633d4226512"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:QZPUDH4PIG354HQCMICUHRTD3K","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Almost weak polynomial stability of operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"D\\'avid Kunszenti-Kov\\'acs","submitted_at":"2012-07-24T21:42:10Z","abstract_excerpt":"We investigate whether almost weak stability of an operator $T$ on a Banach space $X$ implies its almost weak polynomial stability. We show, using a modified version of the van der Corput Lemma that if $X$ is a Hilbert space and $T$ a contraction, then the implication holds. On the other hand, based on a TDS arising from a two dimensional ODE, we give an explicit example of a contraction on a $C_0$ space that is almost weakly stable, but its appropriate polynomial powers fail to converge weakly to zero along a subsequence of density 1. Finally we provide an application to convergence of polyno"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.5835","kind":"arxiv","version":3},"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":"2026-05-18T03:20:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PjmTzZHD+4/S/OdpOwDF/cV4zpoGxK6HBynebFJZqChJ78AdMIENSlKyOMwpoLkSo6en0KAkr+LDjwzARnwDCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T09:40:26.862124Z"},"content_sha256":"fd8c704ea52cf033b4a61e84a397ebf4227ff6c9fa7773a165ef2a64377b437d","schema_version":"1.0","event_id":"sha256:fd8c704ea52cf033b4a61e84a397ebf4227ff6c9fa7773a165ef2a64377b437d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QZPUDH4PIG354HQCMICUHRTD3K/bundle.json","state_url":"https://pith.science/pith/QZPUDH4PIG354HQCMICUHRTD3K/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QZPUDH4PIG354HQCMICUHRTD3K/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":"2026-06-26T09:40:26Z","links":{"resolver":"https://pith.science/pith/QZPUDH4PIG354HQCMICUHRTD3K","bundle":"https://pith.science/pith/QZPUDH4PIG354HQCMICUHRTD3K/bundle.json","state":"https://pith.science/pith/QZPUDH4PIG354HQCMICUHRTD3K/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QZPUDH4PIG354HQCMICUHRTD3K/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:QZPUDH4PIG354HQCMICUHRTD3K","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":"77402d57ca30644d89ac05b031eae3ae527f3eabc05a3fc0f015d66f41bc38c8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2012-07-24T21:42:10Z","title_canon_sha256":"9b4e2525722739087cafc04fa4fa759be22bddcf924e4cebe082bca3c4e25f3f"},"schema_version":"1.0","source":{"id":"1207.5835","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1207.5835","created_at":"2026-05-18T03:20:20Z"},{"alias_kind":"arxiv_version","alias_value":"1207.5835v3","created_at":"2026-05-18T03:20:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1207.5835","created_at":"2026-05-18T03:20:20Z"},{"alias_kind":"pith_short_12","alias_value":"QZPUDH4PIG35","created_at":"2026-05-18T12:27:20Z"},{"alias_kind":"pith_short_16","alias_value":"QZPUDH4PIG354HQC","created_at":"2026-05-18T12:27:20Z"},{"alias_kind":"pith_short_8","alias_value":"QZPUDH4P","created_at":"2026-05-18T12:27:20Z"}],"graph_snapshots":[{"event_id":"sha256:fd8c704ea52cf033b4a61e84a397ebf4227ff6c9fa7773a165ef2a64377b437d","target":"graph","created_at":"2026-05-18T03:20:20Z","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 investigate whether almost weak stability of an operator $T$ on a Banach space $X$ implies its almost weak polynomial stability. We show, using a modified version of the van der Corput Lemma that if $X$ is a Hilbert space and $T$ a contraction, then the implication holds. On the other hand, based on a TDS arising from a two dimensional ODE, we give an explicit example of a contraction on a $C_0$ space that is almost weakly stable, but its appropriate polynomial powers fail to converge weakly to zero along a subsequence of density 1. Finally we provide an application to convergence of polyno","authors_text":"D\\'avid Kunszenti-Kov\\'acs","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2012-07-24T21:42:10Z","title":"Almost weak polynomial stability of operators"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.5835","kind":"arxiv","version":3},"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:adafc7256f9326f9b9fe629b3ba2fbb551517663eb6c4050de477633d4226512","target":"record","created_at":"2026-05-18T03:20:20Z","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":"77402d57ca30644d89ac05b031eae3ae527f3eabc05a3fc0f015d66f41bc38c8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2012-07-24T21:42:10Z","title_canon_sha256":"9b4e2525722739087cafc04fa4fa759be22bddcf924e4cebe082bca3c4e25f3f"},"schema_version":"1.0","source":{"id":"1207.5835","kind":"arxiv","version":3}},"canonical_sha256":"865f419f8f41b7de1e02620543c663da8bd51c3d6762082ef3ecdd0c92032b5c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"865f419f8f41b7de1e02620543c663da8bd51c3d6762082ef3ecdd0c92032b5c","first_computed_at":"2026-05-18T03:20:20.784101Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:20:20.784101Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"3z1PBUFJED3mu0PEArINHbqc+Kz6Q2dCvhDUYbtC2OHRrbny/7zMD0LHDLvxH1VGO1EdWCA6dgctUibIUe9yCA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:20:20.785070Z","signed_message":"canonical_sha256_bytes"},"source_id":"1207.5835","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:adafc7256f9326f9b9fe629b3ba2fbb551517663eb6c4050de477633d4226512","sha256:fd8c704ea52cf033b4a61e84a397ebf4227ff6c9fa7773a165ef2a64377b437d"],"state_sha256":"da4695fa505c7acafd350706a1d70750ef961202d0c146011ba9137f7f9b51d2"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DUivfpFnz7OCGOaVUc5zYoxfqS8yU6Ir+8EMrNZHKK8Y2k4jdBwhujxhaghkcslTWOTBgXh3dHILMeEjB+LGCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-26T09:40:26.864052Z","bundle_sha256":"d1be87fb4f627315c8ac3418ca5e2f8ee82681b58379aac000b10c751f316f0b"}}