{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:3AKDCJDMBUT5F2XS43U2FDG6MV","short_pith_number":"pith:3AKDCJDM","canonical_record":{"source":{"id":"1204.6404","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2012-04-28T12:47:35Z","cross_cats_sorted":[],"title_canon_sha256":"de89fb9b2685c73592ab6cd9a1e44f90ce98179102342ee734c2f56b8118c461","abstract_canon_sha256":"7446c20ff67c6cce6c6eec0356b2224423437aa8f83b71459e0835a0108c87cb"},"schema_version":"1.0"},"canonical_sha256":"d81431246c0d27d2eaf2e6e9a28cde657d90ac5baa8c7cd8d29983bc6d66486d","source":{"kind":"arxiv","id":"1204.6404","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1204.6404","created_at":"2026-05-18T03:56:45Z"},{"alias_kind":"arxiv_version","alias_value":"1204.6404v1","created_at":"2026-05-18T03:56:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1204.6404","created_at":"2026-05-18T03:56:45Z"},{"alias_kind":"pith_short_12","alias_value":"3AKDCJDMBUT5","created_at":"2026-05-18T12:26:50Z"},{"alias_kind":"pith_short_16","alias_value":"3AKDCJDMBUT5F2XS","created_at":"2026-05-18T12:26:50Z"},{"alias_kind":"pith_short_8","alias_value":"3AKDCJDM","created_at":"2026-05-18T12:26:50Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:3AKDCJDMBUT5F2XS43U2FDG6MV","target":"record","payload":{"canonical_record":{"source":{"id":"1204.6404","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2012-04-28T12:47:35Z","cross_cats_sorted":[],"title_canon_sha256":"de89fb9b2685c73592ab6cd9a1e44f90ce98179102342ee734c2f56b8118c461","abstract_canon_sha256":"7446c20ff67c6cce6c6eec0356b2224423437aa8f83b71459e0835a0108c87cb"},"schema_version":"1.0"},"canonical_sha256":"d81431246c0d27d2eaf2e6e9a28cde657d90ac5baa8c7cd8d29983bc6d66486d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:56:45.653132Z","signature_b64":"MBdZasaKDyOlJeWa1mPfSX0E6TZ9wdWQLwvaBp3ZmjF8/oe2gXMmKRYMtuVWxQkAatdgHY1Nq6XXSrw7goqKDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d81431246c0d27d2eaf2e6e9a28cde657d90ac5baa8c7cd8d29983bc6d66486d","last_reissued_at":"2026-05-18T03:56:45.652554Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:56:45.652554Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1204.6404","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":"2026-05-18T03:56:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UcbfjF48pp0ExFZwohStCgKjYFZFxlyxWgdXkseHCLIf6SIwm/rMhESBQqXFVhgwrcF7xuXcHSk8iQE3/5eCCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T15:32:53.019023Z"},"content_sha256":"2b13d1eb9f451c848fdda9e7aeed9bf6dcad27187d07bd522657a0176df1c789","schema_version":"1.0","event_id":"sha256:2b13d1eb9f451c848fdda9e7aeed9bf6dcad27187d07bd522657a0176df1c789"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:3AKDCJDMBUT5F2XS43U2FDG6MV","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Spaceability and algebrability of sets of nowhere integrable functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Leonardo Pellegrini, Pedro L. Kaufmann, Szymon Glab","submitted_at":"2012-04-28T12:47:35Z","abstract_excerpt":"We show that the set of Lebesgue integrable functions in $[0,1]$ which are nowhere essentially bounded is spaceable, improving a result from [F. J. Garc\\'{i}a-Pacheco, M. Mart\\'{i}n, and J. B. Seoane-Sep\\'ulveda. \\textit{Lineability, spaceability, and algebrability of certain subsets of function spaces,} Taiwanese J. Math., \\textbf{13} (2009), no. 4, 1257--1269], and that it is strongly $\\mathfrak{c}$-algebrable. We prove strong $\\mathfrak{c}$-algebrability and non-separable spaceability of the set of functions of bounded variation which have a dense set of jump discontinuities. Applications t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.6404","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":"2026-05-18T03:56:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NBHTjn7mTzDoPkjq7z9vBzFTYtPXjiOLSOaARnnpqgIoq2rjlyZqsPXM/GfzfdyGSPrKHAKhVvwr8ARod/J9DQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T15:32:53.019361Z"},"content_sha256":"87c282989bde4e7dec800b5a6257f2bd127669566e557cd02990f3c54786a6d8","schema_version":"1.0","event_id":"sha256:87c282989bde4e7dec800b5a6257f2bd127669566e557cd02990f3c54786a6d8"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/3AKDCJDMBUT5F2XS43U2FDG6MV/bundle.json","state_url":"https://pith.science/pith/3AKDCJDMBUT5F2XS43U2FDG6MV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/3AKDCJDMBUT5F2XS43U2FDG6MV/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":"2026-06-24T15:32:53Z","links":{"resolver":"https://pith.science/pith/3AKDCJDMBUT5F2XS43U2FDG6MV","bundle":"https://pith.science/pith/3AKDCJDMBUT5F2XS43U2FDG6MV/bundle.json","state":"https://pith.science/pith/3AKDCJDMBUT5F2XS43U2FDG6MV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/3AKDCJDMBUT5F2XS43U2FDG6MV/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:3AKDCJDMBUT5F2XS43U2FDG6MV","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":"7446c20ff67c6cce6c6eec0356b2224423437aa8f83b71459e0835a0108c87cb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2012-04-28T12:47:35Z","title_canon_sha256":"de89fb9b2685c73592ab6cd9a1e44f90ce98179102342ee734c2f56b8118c461"},"schema_version":"1.0","source":{"id":"1204.6404","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1204.6404","created_at":"2026-05-18T03:56:45Z"},{"alias_kind":"arxiv_version","alias_value":"1204.6404v1","created_at":"2026-05-18T03:56:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1204.6404","created_at":"2026-05-18T03:56:45Z"},{"alias_kind":"pith_short_12","alias_value":"3AKDCJDMBUT5","created_at":"2026-05-18T12:26:50Z"},{"alias_kind":"pith_short_16","alias_value":"3AKDCJDMBUT5F2XS","created_at":"2026-05-18T12:26:50Z"},{"alias_kind":"pith_short_8","alias_value":"3AKDCJDM","created_at":"2026-05-18T12:26:50Z"}],"graph_snapshots":[{"event_id":"sha256:87c282989bde4e7dec800b5a6257f2bd127669566e557cd02990f3c54786a6d8","target":"graph","created_at":"2026-05-18T03:56:45Z","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 show that the set of Lebesgue integrable functions in $[0,1]$ which are nowhere essentially bounded is spaceable, improving a result from [F. J. Garc\\'{i}a-Pacheco, M. Mart\\'{i}n, and J. B. Seoane-Sep\\'ulveda. \\textit{Lineability, spaceability, and algebrability of certain subsets of function spaces,} Taiwanese J. Math., \\textbf{13} (2009), no. 4, 1257--1269], and that it is strongly $\\mathfrak{c}$-algebrable. We prove strong $\\mathfrak{c}$-algebrability and non-separable spaceability of the set of functions of bounded variation which have a dense set of jump discontinuities. Applications t","authors_text":"Leonardo Pellegrini, Pedro L. Kaufmann, Szymon Glab","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2012-04-28T12:47:35Z","title":"Spaceability and algebrability of sets of nowhere integrable functions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.6404","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":"sha256:2b13d1eb9f451c848fdda9e7aeed9bf6dcad27187d07bd522657a0176df1c789","target":"record","created_at":"2026-05-18T03:56:45Z","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":"7446c20ff67c6cce6c6eec0356b2224423437aa8f83b71459e0835a0108c87cb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2012-04-28T12:47:35Z","title_canon_sha256":"de89fb9b2685c73592ab6cd9a1e44f90ce98179102342ee734c2f56b8118c461"},"schema_version":"1.0","source":{"id":"1204.6404","kind":"arxiv","version":1}},"canonical_sha256":"d81431246c0d27d2eaf2e6e9a28cde657d90ac5baa8c7cd8d29983bc6d66486d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d81431246c0d27d2eaf2e6e9a28cde657d90ac5baa8c7cd8d29983bc6d66486d","first_computed_at":"2026-05-18T03:56:45.652554Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:56:45.652554Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"MBdZasaKDyOlJeWa1mPfSX0E6TZ9wdWQLwvaBp3ZmjF8/oe2gXMmKRYMtuVWxQkAatdgHY1Nq6XXSrw7goqKDg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:56:45.653132Z","signed_message":"canonical_sha256_bytes"},"source_id":"1204.6404","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2b13d1eb9f451c848fdda9e7aeed9bf6dcad27187d07bd522657a0176df1c789","sha256:87c282989bde4e7dec800b5a6257f2bd127669566e557cd02990f3c54786a6d8"],"state_sha256":"2d42170e0d0d0056d0ad9496c7403edc588681897072cb48082cf4c0c0b924a7"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"A3nNOtpycrHYYYdV2HNNZQUC2QZuy3pOSxRfvttBMsxtyrQ4SnC2R7h3mYAXn7HQUTZXi3v7nL/567+ln8APCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-24T15:32:53.021512Z","bundle_sha256":"e0a16f2488f7aaf3e459d1cf23ca335609d1cc74e3a77f959cbcb4c18aac5860"}}