{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:ZBELYGILBIFG6BHRJTS3B3B25T","short_pith_number":"pith:ZBELYGIL","canonical_record":{"source":{"id":"1604.02555","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2016-04-09T12:23:45Z","cross_cats_sorted":["math.GN"],"title_canon_sha256":"c35e512d985b29199d3a3e4db8404abf65771fbbe8a2a84527abd99a140a463c","abstract_canon_sha256":"cee95255f79474450a6d3e82adcfe94f7920e15500c7710affdc9213d79a787d"},"schema_version":"1.0"},"canonical_sha256":"c848bc190b0a0a6f04f14ce5b0ec3aecfaf4eaccf6d63da2239faee84e2a8d5b","source":{"kind":"arxiv","id":"1604.02555","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1604.02555","created_at":"2026-05-18T01:16:59Z"},{"alias_kind":"arxiv_version","alias_value":"1604.02555v2","created_at":"2026-05-18T01:16:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1604.02555","created_at":"2026-05-18T01:16:59Z"},{"alias_kind":"pith_short_12","alias_value":"ZBELYGILBIFG","created_at":"2026-05-18T12:30:53Z"},{"alias_kind":"pith_short_16","alias_value":"ZBELYGILBIFG6BHR","created_at":"2026-05-18T12:30:53Z"},{"alias_kind":"pith_short_8","alias_value":"ZBELYGIL","created_at":"2026-05-18T12:30:53Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:ZBELYGILBIFG6BHRJTS3B3B25T","target":"record","payload":{"canonical_record":{"source":{"id":"1604.02555","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2016-04-09T12:23:45Z","cross_cats_sorted":["math.GN"],"title_canon_sha256":"c35e512d985b29199d3a3e4db8404abf65771fbbe8a2a84527abd99a140a463c","abstract_canon_sha256":"cee95255f79474450a6d3e82adcfe94f7920e15500c7710affdc9213d79a787d"},"schema_version":"1.0"},"canonical_sha256":"c848bc190b0a0a6f04f14ce5b0ec3aecfaf4eaccf6d63da2239faee84e2a8d5b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:16:59.246925Z","signature_b64":"xac82AoZA0OjzI1apC3UEUkR7XEbDL+p9UpC9mHuVzWjeTWhHQ7Nx2aIS1+OfN0pQJjNI4PCU6SBWtWuxjcyBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c848bc190b0a0a6f04f14ce5b0ec3aecfaf4eaccf6d63da2239faee84e2a8d5b","last_reissued_at":"2026-05-18T01:16:59.246149Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:16:59.246149Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1604.02555","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:16:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qeF6SJPMIA78lm0fWdDr3M+A60LbQOlYMIW2Jl94SiiYmOkijLZkKTNgli27KsezNafmIb58X1TWdyWwBr37Aw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T16:25:46.751306Z"},"content_sha256":"665d5c8872b841c1fe29822b37c86198ad05e8ceb443f045f510a326f708eb1e","schema_version":"1.0","event_id":"sha256:665d5c8872b841c1fe29822b37c86198ad05e8ceb443f045f510a326f708eb1e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:ZBELYGILBIFG6BHRJTS3B3B25T","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Free locally convex spaces with a small base","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GN"],"primary_cat":"math.FA","authors_text":"Jerzy Kakol, Saak Gabriyelyan","submitted_at":"2016-04-09T12:23:45Z","abstract_excerpt":"The paper studies the free locally convex space $L(X)$ over a Tychonoff space $X$. Since for infinite $X$ the space $L(X)$ is never metrizable (even not Fr\\'echet-Urysohn), a possible applicable generalized metric property for $L(X)$ is welcome. We propose a concept (essentially weaker than first-countability) which is known under the name a $\\mathfrak{G}$-base. A space $X$ has a {\\em $\\mathfrak{G}$-base} if for every $x\\in X$ there is a base $\\{ U_\\alpha : \\alpha\\in\\mathbb{N}^\\mathbb{N}\\}$ of neighborhoods at $x$ such that $U_\\beta \\subseteq U_\\alpha$ whenever $\\alpha\\leq\\beta$ for all $\\alph"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.02555","kind":"arxiv","version":2},"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":"2026-05-18T01:16:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5iP46X+JatQcutLW7WALkRl6BlAUiZkimRMghdGXncg0WbsMqQLI7szNiYnWu0eWkTG66lzzBdq1F25kOR1uAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T16:25:46.751988Z"},"content_sha256":"9b82dddd1d947031a4874cae15194fe35375d980dfac845e1a154ed1b3abcc0f","schema_version":"1.0","event_id":"sha256:9b82dddd1d947031a4874cae15194fe35375d980dfac845e1a154ed1b3abcc0f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ZBELYGILBIFG6BHRJTS3B3B25T/bundle.json","state_url":"https://pith.science/pith/ZBELYGILBIFG6BHRJTS3B3B25T/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ZBELYGILBIFG6BHRJTS3B3B25T/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":"2026-06-06T16:25:46Z","links":{"resolver":"https://pith.science/pith/ZBELYGILBIFG6BHRJTS3B3B25T","bundle":"https://pith.science/pith/ZBELYGILBIFG6BHRJTS3B3B25T/bundle.json","state":"https://pith.science/pith/ZBELYGILBIFG6BHRJTS3B3B25T/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ZBELYGILBIFG6BHRJTS3B3B25T/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:ZBELYGILBIFG6BHRJTS3B3B25T","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":"cee95255f79474450a6d3e82adcfe94f7920e15500c7710affdc9213d79a787d","cross_cats_sorted":["math.GN"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2016-04-09T12:23:45Z","title_canon_sha256":"c35e512d985b29199d3a3e4db8404abf65771fbbe8a2a84527abd99a140a463c"},"schema_version":"1.0","source":{"id":"1604.02555","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1604.02555","created_at":"2026-05-18T01:16:59Z"},{"alias_kind":"arxiv_version","alias_value":"1604.02555v2","created_at":"2026-05-18T01:16:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1604.02555","created_at":"2026-05-18T01:16:59Z"},{"alias_kind":"pith_short_12","alias_value":"ZBELYGILBIFG","created_at":"2026-05-18T12:30:53Z"},{"alias_kind":"pith_short_16","alias_value":"ZBELYGILBIFG6BHR","created_at":"2026-05-18T12:30:53Z"},{"alias_kind":"pith_short_8","alias_value":"ZBELYGIL","created_at":"2026-05-18T12:30:53Z"}],"graph_snapshots":[{"event_id":"sha256:9b82dddd1d947031a4874cae15194fe35375d980dfac845e1a154ed1b3abcc0f","target":"graph","created_at":"2026-05-18T01:16:59Z","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 studies the free locally convex space $L(X)$ over a Tychonoff space $X$. Since for infinite $X$ the space $L(X)$ is never metrizable (even not Fr\\'echet-Urysohn), a possible applicable generalized metric property for $L(X)$ is welcome. We propose a concept (essentially weaker than first-countability) which is known under the name a $\\mathfrak{G}$-base. A space $X$ has a {\\em $\\mathfrak{G}$-base} if for every $x\\in X$ there is a base $\\{ U_\\alpha : \\alpha\\in\\mathbb{N}^\\mathbb{N}\\}$ of neighborhoods at $x$ such that $U_\\beta \\subseteq U_\\alpha$ whenever $\\alpha\\leq\\beta$ for all $\\alph","authors_text":"Jerzy Kakol, Saak Gabriyelyan","cross_cats":["math.GN"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2016-04-09T12:23:45Z","title":"Free locally convex spaces with a small base"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.02555","kind":"arxiv","version":2},"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":"sha256:665d5c8872b841c1fe29822b37c86198ad05e8ceb443f045f510a326f708eb1e","target":"record","created_at":"2026-05-18T01:16:59Z","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":"cee95255f79474450a6d3e82adcfe94f7920e15500c7710affdc9213d79a787d","cross_cats_sorted":["math.GN"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2016-04-09T12:23:45Z","title_canon_sha256":"c35e512d985b29199d3a3e4db8404abf65771fbbe8a2a84527abd99a140a463c"},"schema_version":"1.0","source":{"id":"1604.02555","kind":"arxiv","version":2}},"canonical_sha256":"c848bc190b0a0a6f04f14ce5b0ec3aecfaf4eaccf6d63da2239faee84e2a8d5b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c848bc190b0a0a6f04f14ce5b0ec3aecfaf4eaccf6d63da2239faee84e2a8d5b","first_computed_at":"2026-05-18T01:16:59.246149Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:16:59.246149Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"xac82AoZA0OjzI1apC3UEUkR7XEbDL+p9UpC9mHuVzWjeTWhHQ7Nx2aIS1+OfN0pQJjNI4PCU6SBWtWuxjcyBg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:16:59.246925Z","signed_message":"canonical_sha256_bytes"},"source_id":"1604.02555","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:665d5c8872b841c1fe29822b37c86198ad05e8ceb443f045f510a326f708eb1e","sha256:9b82dddd1d947031a4874cae15194fe35375d980dfac845e1a154ed1b3abcc0f"],"state_sha256":"617be60f36a80d133b8e6aed8f1d2ce422654b858e8c958c9bb115a239a4cb53"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kpop6OKFw3u8q6PJ7mZ5dzlMWTwA8aWq0GNDwT+1ac9qy66F8WJE3gvy/pDRhD8IHRMyEFMJTkv16pz5d5y4BQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-06T16:25:46.755620Z","bundle_sha256":"b8b0817f8c3ffc266f070007c1a898987ad0ce5a27b82bd38f095b48a5cc12b2"}}