{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:Z3QXKD6L7CSD25CEHPH4NQOXGP","short_pith_number":"pith:Z3QXKD6L","canonical_record":{"source":{"id":"1507.04912","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2015-07-17T10:44:20Z","cross_cats_sorted":["math.GN"],"title_canon_sha256":"4c18651839bb66299bfbe9152c7f4895575fb6c5c590433093e12e487f1ef781","abstract_canon_sha256":"86fe139bc4cc2617c8a8b30490d467b3ea805a3d0068fb06dac7c38e7be9a160"},"schema_version":"1.0"},"canonical_sha256":"cee1750fcbf8a43d74443bcfc6c1d733ccc7f1c2838db55989ab4e9ba6b8f7d0","source":{"kind":"arxiv","id":"1507.04912","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1507.04912","created_at":"2026-05-18T01:32:36Z"},{"alias_kind":"arxiv_version","alias_value":"1507.04912v2","created_at":"2026-05-18T01:32:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.04912","created_at":"2026-05-18T01:32:36Z"},{"alias_kind":"pith_short_12","alias_value":"Z3QXKD6L7CSD","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_16","alias_value":"Z3QXKD6L7CSD25CE","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_8","alias_value":"Z3QXKD6L","created_at":"2026-05-18T12:29:52Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:Z3QXKD6L7CSD25CEHPH4NQOXGP","target":"record","payload":{"canonical_record":{"source":{"id":"1507.04912","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2015-07-17T10:44:20Z","cross_cats_sorted":["math.GN"],"title_canon_sha256":"4c18651839bb66299bfbe9152c7f4895575fb6c5c590433093e12e487f1ef781","abstract_canon_sha256":"86fe139bc4cc2617c8a8b30490d467b3ea805a3d0068fb06dac7c38e7be9a160"},"schema_version":"1.0"},"canonical_sha256":"cee1750fcbf8a43d74443bcfc6c1d733ccc7f1c2838db55989ab4e9ba6b8f7d0","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:32:36.872622Z","signature_b64":"RwVZlLaOqyHqBT3RTni1qD/ROQq2D0R34e4ASOgjKHy1xP9voNK4xqrHKL0wyfaTbzegHOa01G7SDsL327e1Cw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cee1750fcbf8a43d74443bcfc6c1d733ccc7f1c2838db55989ab4e9ba6b8f7d0","last_reissued_at":"2026-05-18T01:32:36.872089Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:32:36.872089Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1507.04912","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":"2026-05-18T01:32:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zXZKX4+/Zls7ise0D9NxRgwGHGO74Ub4EtjeTwOABwmgOtodnB7mkreCO8xG//Ur05bhH0Tf7j6fqQT0UspMBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T19:00:46.309517Z"},"content_sha256":"2d374efe0dc1a55c8ca59c73ff9606cb28684f4ed6350872a6fc7fbb0e313455","schema_version":"1.0","event_id":"sha256:2d374efe0dc1a55c8ca59c73ff9606cb28684f4ed6350872a6fc7fbb0e313455"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:Z3QXKD6L7CSD25CEHPH4NQOXGP","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The topological properties of $q$-spaces in free topological groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GN"],"primary_cat":"math.GR","authors_text":"Chuan Liu, Fucai Lin, Shou Lin","submitted_at":"2015-07-17T10:44:20Z","abstract_excerpt":"Given a Tychonoff space $X$, let $F(X)$ and $A(X)$ be respectively the free topological group and the free Abelian topological group over $X$ in the sense of Markov. In this paper, we provide some topological properties of $X$ whenever one of $F(X)$, $A(X)$, some finite level of $F(X)$ and some finite level of $A(X)$ is $q$-space (in particular, locally $\\omega$-bounded spaces and $r$-spaces), which give some partial answers to a problem posed in [11]."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.04912","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":"2026-05-18T01:32:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hWaYhBsHJS+srdFChT/9ucwZ8elRswvBd5hScAZQ7IXdl5UA7XTqECkoBtwSeX9sl1RgoqWZdVV/tm7OjWr0CQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T19:00:46.310210Z"},"content_sha256":"58ed11f3166611ba5ef781856405c08529d3fc5431494c4ed0d076248b42b24f","schema_version":"1.0","event_id":"sha256:58ed11f3166611ba5ef781856405c08529d3fc5431494c4ed0d076248b42b24f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/Z3QXKD6L7CSD25CEHPH4NQOXGP/bundle.json","state_url":"https://pith.science/pith/Z3QXKD6L7CSD25CEHPH4NQOXGP/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/Z3QXKD6L7CSD25CEHPH4NQOXGP/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":"2026-06-06T19:00:46Z","links":{"resolver":"https://pith.science/pith/Z3QXKD6L7CSD25CEHPH4NQOXGP","bundle":"https://pith.science/pith/Z3QXKD6L7CSD25CEHPH4NQOXGP/bundle.json","state":"https://pith.science/pith/Z3QXKD6L7CSD25CEHPH4NQOXGP/state.json","well_known_bundle":"https://pith.science/.well-known/pith/Z3QXKD6L7CSD25CEHPH4NQOXGP/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:Z3QXKD6L7CSD25CEHPH4NQOXGP","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":"86fe139bc4cc2617c8a8b30490d467b3ea805a3d0068fb06dac7c38e7be9a160","cross_cats_sorted":["math.GN"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2015-07-17T10:44:20Z","title_canon_sha256":"4c18651839bb66299bfbe9152c7f4895575fb6c5c590433093e12e487f1ef781"},"schema_version":"1.0","source":{"id":"1507.04912","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1507.04912","created_at":"2026-05-18T01:32:36Z"},{"alias_kind":"arxiv_version","alias_value":"1507.04912v2","created_at":"2026-05-18T01:32:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.04912","created_at":"2026-05-18T01:32:36Z"},{"alias_kind":"pith_short_12","alias_value":"Z3QXKD6L7CSD","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_16","alias_value":"Z3QXKD6L7CSD25CE","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_8","alias_value":"Z3QXKD6L","created_at":"2026-05-18T12:29:52Z"}],"graph_snapshots":[{"event_id":"sha256:58ed11f3166611ba5ef781856405c08529d3fc5431494c4ed0d076248b42b24f","target":"graph","created_at":"2026-05-18T01:32:36Z","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":"Given a Tychonoff space $X$, let $F(X)$ and $A(X)$ be respectively the free topological group and the free Abelian topological group over $X$ in the sense of Markov. In this paper, we provide some topological properties of $X$ whenever one of $F(X)$, $A(X)$, some finite level of $F(X)$ and some finite level of $A(X)$ is $q$-space (in particular, locally $\\omega$-bounded spaces and $r$-spaces), which give some partial answers to a problem posed in [11].","authors_text":"Chuan Liu, Fucai Lin, Shou Lin","cross_cats":["math.GN"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2015-07-17T10:44:20Z","title":"The topological properties of $q$-spaces in free topological groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.04912","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":"sha256:2d374efe0dc1a55c8ca59c73ff9606cb28684f4ed6350872a6fc7fbb0e313455","target":"record","created_at":"2026-05-18T01:32:36Z","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":"86fe139bc4cc2617c8a8b30490d467b3ea805a3d0068fb06dac7c38e7be9a160","cross_cats_sorted":["math.GN"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2015-07-17T10:44:20Z","title_canon_sha256":"4c18651839bb66299bfbe9152c7f4895575fb6c5c590433093e12e487f1ef781"},"schema_version":"1.0","source":{"id":"1507.04912","kind":"arxiv","version":2}},"canonical_sha256":"cee1750fcbf8a43d74443bcfc6c1d733ccc7f1c2838db55989ab4e9ba6b8f7d0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cee1750fcbf8a43d74443bcfc6c1d733ccc7f1c2838db55989ab4e9ba6b8f7d0","first_computed_at":"2026-05-18T01:32:36.872089Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:32:36.872089Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"RwVZlLaOqyHqBT3RTni1qD/ROQq2D0R34e4ASOgjKHy1xP9voNK4xqrHKL0wyfaTbzegHOa01G7SDsL327e1Cw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:32:36.872622Z","signed_message":"canonical_sha256_bytes"},"source_id":"1507.04912","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2d374efe0dc1a55c8ca59c73ff9606cb28684f4ed6350872a6fc7fbb0e313455","sha256:58ed11f3166611ba5ef781856405c08529d3fc5431494c4ed0d076248b42b24f"],"state_sha256":"82af68869ea484368050b5db2b6f744adb712c4eebffe630931f68d67254fc09"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lBnqwptVTMShuO/0U7SuUeZyvMUptz10m5Yzj6bMWxt1rtXp/uV+6tPNQ6wB39AZyqcdVf34gBcfqu0l7S7QCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-06T19:00:46.313978Z","bundle_sha256":"5446d443241efb53a891821954d831f2cdb7f1aa7980f85e6bf9634279103f43"}}