{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:XTM6LHLKFOULO4G6CLSPC76JG4","short_pith_number":"pith:XTM6LHLK","canonical_record":{"source":{"id":"1710.03990","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2017-10-11T10:19:35Z","cross_cats_sorted":["math.AP","math.CA"],"title_canon_sha256":"60ced9201d101fd527526bf894e3dddda6c5370ae092a1c36c3ef83eb2b0ba9f","abstract_canon_sha256":"b76eb33ba28b3f751760abec83e11e4053fb63db00f731658597b0531551599e"},"schema_version":"1.0"},"canonical_sha256":"bcd9e59d6a2ba8b770de12e4f17fc9372f71443b47b1fbc0acca7dde664603b4","source":{"kind":"arxiv","id":"1710.03990","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1710.03990","created_at":"2026-05-18T00:33:05Z"},{"alias_kind":"arxiv_version","alias_value":"1710.03990v1","created_at":"2026-05-18T00:33:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1710.03990","created_at":"2026-05-18T00:33:05Z"},{"alias_kind":"pith_short_12","alias_value":"XTM6LHLKFOUL","created_at":"2026-05-18T12:31:56Z"},{"alias_kind":"pith_short_16","alias_value":"XTM6LHLKFOULO4G6","created_at":"2026-05-18T12:31:56Z"},{"alias_kind":"pith_short_8","alias_value":"XTM6LHLK","created_at":"2026-05-18T12:31:56Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:XTM6LHLKFOULO4G6CLSPC76JG4","target":"record","payload":{"canonical_record":{"source":{"id":"1710.03990","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2017-10-11T10:19:35Z","cross_cats_sorted":["math.AP","math.CA"],"title_canon_sha256":"60ced9201d101fd527526bf894e3dddda6c5370ae092a1c36c3ef83eb2b0ba9f","abstract_canon_sha256":"b76eb33ba28b3f751760abec83e11e4053fb63db00f731658597b0531551599e"},"schema_version":"1.0"},"canonical_sha256":"bcd9e59d6a2ba8b770de12e4f17fc9372f71443b47b1fbc0acca7dde664603b4","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:33:05.379733Z","signature_b64":"DqZZrFJ+BL52QWLFmPlU1FgsIAK3Xwu6VEDSHVLg2JL07QCXXH+m6QU9fexFRJW5X1DYYARt56AvssDA8SkWAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bcd9e59d6a2ba8b770de12e4f17fc9372f71443b47b1fbc0acca7dde664603b4","last_reissued_at":"2026-05-18T00:33:05.379250Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:33:05.379250Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1710.03990","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":"2026-05-18T00:33:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"swijEhEZBRj3oYf9DG7R46Mi//tYl7mGogu28OlgKKvT2I8rKSF4gaip97vlTP9scrnX3dACMtN5aZ3LaZA6CQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T17:16:56.351279Z"},"content_sha256":"e62df658f2e9c6bd1a1f1b47ecb0464dd756e6552a4047c78b1603f64fc6e20e","schema_version":"1.0","event_id":"sha256:e62df658f2e9c6bd1a1f1b47ecb0464dd756e6552a4047c78b1603f64fc6e20e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:XTM6LHLKFOULO4G6CLSPC76JG4","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Construction of function spaces close to $L^\\infty$ with associate space close to $L^1$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","math.CA"],"primary_cat":"math.FA","authors_text":"Amiran Gogatishvili, David Edmunds, Tengiz Kopaliani","submitted_at":"2017-10-11T10:19:35Z","abstract_excerpt":"The paper introduces a variable exponent space $X$ which has in common with $L^{\\infty}([0,1])$ the property that the space $C([0,1])$ of continuous functions on $[0,1]$ is a closed linear subspace in it. The associate space of $X$ contains both the Kolmogorov and the Marcinkiewicz examples of functions in $L^{1}$ with a.e. divergent Fourier series."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.03990","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":"2026-05-18T00:33:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JQyY7OnWHI3yOwlPmXafWTkNY/qyzgZchOXIbjdF4rtuo/BEaNJ3ZD2Teq8dCd0z7GIyJBBc18vUqT4TtLEgBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T17:16:56.351632Z"},"content_sha256":"6af9be2cfdbda6fc744a039daa06646070ace2e09ebe348d601b82580e756845","schema_version":"1.0","event_id":"sha256:6af9be2cfdbda6fc744a039daa06646070ace2e09ebe348d601b82580e756845"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/XTM6LHLKFOULO4G6CLSPC76JG4/bundle.json","state_url":"https://pith.science/pith/XTM6LHLKFOULO4G6CLSPC76JG4/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/XTM6LHLKFOULO4G6CLSPC76JG4/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":"2026-06-27T17:16:56Z","links":{"resolver":"https://pith.science/pith/XTM6LHLKFOULO4G6CLSPC76JG4","bundle":"https://pith.science/pith/XTM6LHLKFOULO4G6CLSPC76JG4/bundle.json","state":"https://pith.science/pith/XTM6LHLKFOULO4G6CLSPC76JG4/state.json","well_known_bundle":"https://pith.science/.well-known/pith/XTM6LHLKFOULO4G6CLSPC76JG4/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:XTM6LHLKFOULO4G6CLSPC76JG4","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":"b76eb33ba28b3f751760abec83e11e4053fb63db00f731658597b0531551599e","cross_cats_sorted":["math.AP","math.CA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2017-10-11T10:19:35Z","title_canon_sha256":"60ced9201d101fd527526bf894e3dddda6c5370ae092a1c36c3ef83eb2b0ba9f"},"schema_version":"1.0","source":{"id":"1710.03990","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1710.03990","created_at":"2026-05-18T00:33:05Z"},{"alias_kind":"arxiv_version","alias_value":"1710.03990v1","created_at":"2026-05-18T00:33:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1710.03990","created_at":"2026-05-18T00:33:05Z"},{"alias_kind":"pith_short_12","alias_value":"XTM6LHLKFOUL","created_at":"2026-05-18T12:31:56Z"},{"alias_kind":"pith_short_16","alias_value":"XTM6LHLKFOULO4G6","created_at":"2026-05-18T12:31:56Z"},{"alias_kind":"pith_short_8","alias_value":"XTM6LHLK","created_at":"2026-05-18T12:31:56Z"}],"graph_snapshots":[{"event_id":"sha256:6af9be2cfdbda6fc744a039daa06646070ace2e09ebe348d601b82580e756845","target":"graph","created_at":"2026-05-18T00:33:05Z","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 paper introduces a variable exponent space $X$ which has in common with $L^{\\infty}([0,1])$ the property that the space $C([0,1])$ of continuous functions on $[0,1]$ is a closed linear subspace in it. The associate space of $X$ contains both the Kolmogorov and the Marcinkiewicz examples of functions in $L^{1}$ with a.e. divergent Fourier series.","authors_text":"Amiran Gogatishvili, David Edmunds, Tengiz Kopaliani","cross_cats":["math.AP","math.CA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2017-10-11T10:19:35Z","title":"Construction of function spaces close to $L^\\infty$ with associate space close to $L^1$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.03990","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:e62df658f2e9c6bd1a1f1b47ecb0464dd756e6552a4047c78b1603f64fc6e20e","target":"record","created_at":"2026-05-18T00:33:05Z","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":"b76eb33ba28b3f751760abec83e11e4053fb63db00f731658597b0531551599e","cross_cats_sorted":["math.AP","math.CA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2017-10-11T10:19:35Z","title_canon_sha256":"60ced9201d101fd527526bf894e3dddda6c5370ae092a1c36c3ef83eb2b0ba9f"},"schema_version":"1.0","source":{"id":"1710.03990","kind":"arxiv","version":1}},"canonical_sha256":"bcd9e59d6a2ba8b770de12e4f17fc9372f71443b47b1fbc0acca7dde664603b4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bcd9e59d6a2ba8b770de12e4f17fc9372f71443b47b1fbc0acca7dde664603b4","first_computed_at":"2026-05-18T00:33:05.379250Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:33:05.379250Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"DqZZrFJ+BL52QWLFmPlU1FgsIAK3Xwu6VEDSHVLg2JL07QCXXH+m6QU9fexFRJW5X1DYYARt56AvssDA8SkWAw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:33:05.379733Z","signed_message":"canonical_sha256_bytes"},"source_id":"1710.03990","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e62df658f2e9c6bd1a1f1b47ecb0464dd756e6552a4047c78b1603f64fc6e20e","sha256:6af9be2cfdbda6fc744a039daa06646070ace2e09ebe348d601b82580e756845"],"state_sha256":"299f7ccda1b1c47540c7f1a83b33d435c491792bc56a204b045cb1346e16156d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5Z1Rb7u899vp6k85zc+G2zyDeYuhEUyMcqEKp8+6jInMbIkqZg9HkNUzby99iN9pvPG3kOQvbzdcf8b8UjvYAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-27T17:16:56.353393Z","bundle_sha256":"d7ee46e3783a5e9b4b4952ecfe42e95158807273d628f049b5d3d6f73776568f"}}