{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:NGH3FQVZK33RMDGPDVW7D5K5PG","short_pith_number":"pith:NGH3FQVZ","canonical_record":{"source":{"id":"1309.1965","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2013-09-08T15:12:26Z","cross_cats_sorted":[],"title_canon_sha256":"3a32561d55c03477e8a599b5fc5c4ded9b0e55aa4bc957c984423c236a2d421f","abstract_canon_sha256":"6af24f260903ed4c2d7b0e817211ae5665834b7ac60332615fea9e9f56b7c7a4"},"schema_version":"1.0"},"canonical_sha256":"698fb2c2b956f7160ccf1d6df1f55d798ec0dd8e2aa5816a2fa6ec167ffe9488","source":{"kind":"arxiv","id":"1309.1965","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1309.1965","created_at":"2026-05-18T03:13:56Z"},{"alias_kind":"arxiv_version","alias_value":"1309.1965v1","created_at":"2026-05-18T03:13:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.1965","created_at":"2026-05-18T03:13:56Z"},{"alias_kind":"pith_short_12","alias_value":"NGH3FQVZK33R","created_at":"2026-05-18T12:27:52Z"},{"alias_kind":"pith_short_16","alias_value":"NGH3FQVZK33RMDGP","created_at":"2026-05-18T12:27:52Z"},{"alias_kind":"pith_short_8","alias_value":"NGH3FQVZ","created_at":"2026-05-18T12:27:52Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:NGH3FQVZK33RMDGPDVW7D5K5PG","target":"record","payload":{"canonical_record":{"source":{"id":"1309.1965","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2013-09-08T15:12:26Z","cross_cats_sorted":[],"title_canon_sha256":"3a32561d55c03477e8a599b5fc5c4ded9b0e55aa4bc957c984423c236a2d421f","abstract_canon_sha256":"6af24f260903ed4c2d7b0e817211ae5665834b7ac60332615fea9e9f56b7c7a4"},"schema_version":"1.0"},"canonical_sha256":"698fb2c2b956f7160ccf1d6df1f55d798ec0dd8e2aa5816a2fa6ec167ffe9488","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:13:56.891829Z","signature_b64":"b38zwMYpeDpn3bUW2lqwbkscA390rOkbC1eqROjUmE+s1pLPbtkBnhsmnDIgRBi86NzHENMQo2fMhcyBZBDLBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"698fb2c2b956f7160ccf1d6df1f55d798ec0dd8e2aa5816a2fa6ec167ffe9488","last_reissued_at":"2026-05-18T03:13:56.891102Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:13:56.891102Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1309.1965","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":"2026-05-18T03:13:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0AaLV1QmAGjTQlsBBa4WqrmgC4B3Qt3f/TawRB/vihDLTzb7sOgkS30JarmofjTvTI51KW7YhdhsSrPK7eKJBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T18:59:06.775180Z"},"content_sha256":"ecb5cc8bf93153bc52ac4760a019ab9eca9ed7ff454b25c4d7bcde6bad892d33","schema_version":"1.0","event_id":"sha256:ecb5cc8bf93153bc52ac4760a019ab9eca9ed7ff454b25c4d7bcde6bad892d33"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:NGH3FQVZK33RMDGPDVW7D5K5PG","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Lineability, spaceability, and additivity cardinals for Darboux-like functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Daniel Pellegrino, Jos\\'e L. G\\'amez-Merino, Juan B. Seoane-Sep\\'ulveda, Krzysztof Chris Ciesielski","submitted_at":"2013-09-08T15:12:26Z","abstract_excerpt":"We introduce the concept of {\\em maximal lineability cardinal number}, $\\mL(M)$, of a subset $M$ of a topological vector space and study its relation to the cardinal numbers known as: additivity $A(M)$, homogeneous lineability $\\HL(M)$, and lineability $\\LL(M)$ of $M$. In particular, we will describe, in terms of $\\LL$, the lineability and spaceability of the families of the following Darboux-like functions on $\\real^n$, $n\\ge 1$: extendable, Jones, and almost continuous functions."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.1965","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":"2026-05-18T03:13:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pPdbMbXQNq5FhmZwPBkAGrNVDjoFG5G4+IQAL762B+iXkYSSXE9vJEg8OgOVLEtG+0vkiF63sa3at53c7mdKCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T18:59:06.775674Z"},"content_sha256":"27a1bf6e859ca51d4b2d92e6976a7d70a099d272afae70026f2da66704e1f352","schema_version":"1.0","event_id":"sha256:27a1bf6e859ca51d4b2d92e6976a7d70a099d272afae70026f2da66704e1f352"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NGH3FQVZK33RMDGPDVW7D5K5PG/bundle.json","state_url":"https://pith.science/pith/NGH3FQVZK33RMDGPDVW7D5K5PG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NGH3FQVZK33RMDGPDVW7D5K5PG/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":"2026-06-23T18:59:06Z","links":{"resolver":"https://pith.science/pith/NGH3FQVZK33RMDGPDVW7D5K5PG","bundle":"https://pith.science/pith/NGH3FQVZK33RMDGPDVW7D5K5PG/bundle.json","state":"https://pith.science/pith/NGH3FQVZK33RMDGPDVW7D5K5PG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NGH3FQVZK33RMDGPDVW7D5K5PG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:NGH3FQVZK33RMDGPDVW7D5K5PG","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":"6af24f260903ed4c2d7b0e817211ae5665834b7ac60332615fea9e9f56b7c7a4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2013-09-08T15:12:26Z","title_canon_sha256":"3a32561d55c03477e8a599b5fc5c4ded9b0e55aa4bc957c984423c236a2d421f"},"schema_version":"1.0","source":{"id":"1309.1965","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1309.1965","created_at":"2026-05-18T03:13:56Z"},{"alias_kind":"arxiv_version","alias_value":"1309.1965v1","created_at":"2026-05-18T03:13:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.1965","created_at":"2026-05-18T03:13:56Z"},{"alias_kind":"pith_short_12","alias_value":"NGH3FQVZK33R","created_at":"2026-05-18T12:27:52Z"},{"alias_kind":"pith_short_16","alias_value":"NGH3FQVZK33RMDGP","created_at":"2026-05-18T12:27:52Z"},{"alias_kind":"pith_short_8","alias_value":"NGH3FQVZ","created_at":"2026-05-18T12:27:52Z"}],"graph_snapshots":[{"event_id":"sha256:27a1bf6e859ca51d4b2d92e6976a7d70a099d272afae70026f2da66704e1f352","target":"graph","created_at":"2026-05-18T03:13:56Z","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 introduce the concept of {\\em maximal lineability cardinal number}, $\\mL(M)$, of a subset $M$ of a topological vector space and study its relation to the cardinal numbers known as: additivity $A(M)$, homogeneous lineability $\\HL(M)$, and lineability $\\LL(M)$ of $M$. In particular, we will describe, in terms of $\\LL$, the lineability and spaceability of the families of the following Darboux-like functions on $\\real^n$, $n\\ge 1$: extendable, Jones, and almost continuous functions.","authors_text":"Daniel Pellegrino, Jos\\'e L. G\\'amez-Merino, Juan B. Seoane-Sep\\'ulveda, Krzysztof Chris Ciesielski","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2013-09-08T15:12:26Z","title":"Lineability, spaceability, and additivity cardinals for Darboux-like functions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.1965","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:ecb5cc8bf93153bc52ac4760a019ab9eca9ed7ff454b25c4d7bcde6bad892d33","target":"record","created_at":"2026-05-18T03:13:56Z","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":"6af24f260903ed4c2d7b0e817211ae5665834b7ac60332615fea9e9f56b7c7a4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2013-09-08T15:12:26Z","title_canon_sha256":"3a32561d55c03477e8a599b5fc5c4ded9b0e55aa4bc957c984423c236a2d421f"},"schema_version":"1.0","source":{"id":"1309.1965","kind":"arxiv","version":1}},"canonical_sha256":"698fb2c2b956f7160ccf1d6df1f55d798ec0dd8e2aa5816a2fa6ec167ffe9488","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"698fb2c2b956f7160ccf1d6df1f55d798ec0dd8e2aa5816a2fa6ec167ffe9488","first_computed_at":"2026-05-18T03:13:56.891102Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:13:56.891102Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"b38zwMYpeDpn3bUW2lqwbkscA390rOkbC1eqROjUmE+s1pLPbtkBnhsmnDIgRBi86NzHENMQo2fMhcyBZBDLBg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:13:56.891829Z","signed_message":"canonical_sha256_bytes"},"source_id":"1309.1965","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ecb5cc8bf93153bc52ac4760a019ab9eca9ed7ff454b25c4d7bcde6bad892d33","sha256:27a1bf6e859ca51d4b2d92e6976a7d70a099d272afae70026f2da66704e1f352"],"state_sha256":"49b8846326fa14226d705f5500a541dc8aefebe77981d8cbf8bea18b73bb9280"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8LLySrH2bBOyziCU5sRSjiijSfDlkN7lMvSgEANY9DG+7qaU4pmtnyolmt4bggFMcz49hfy7fCqgeBfTSlYLDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T18:59:06.778203Z","bundle_sha256":"70062a005a5a18f548f9ccef71cb28847298db9a4099dcdaaed8ad1aa4f9a787"}}