{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:2TJHBUPCEXTTHGYOLJJE4VR5W7","short_pith_number":"pith:2TJHBUPC","canonical_record":{"source":{"id":"1312.4750","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2013-12-17T12:39:35Z","cross_cats_sorted":[],"title_canon_sha256":"085ee890b35733daa92cfac3c22524174f8e2173f556e715c70a085ea7518224","abstract_canon_sha256":"8fbb4429c467312221e4b1be881df0483ff9baf29eec21eb2cd0e555c667c760"},"schema_version":"1.0"},"canonical_sha256":"d4d270d1e225e7339b0e5a524e563db7de7566ee1b85e7431a18398b75b73682","source":{"kind":"arxiv","id":"1312.4750","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1312.4750","created_at":"2026-05-18T01:53:09Z"},{"alias_kind":"arxiv_version","alias_value":"1312.4750v2","created_at":"2026-05-18T01:53:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1312.4750","created_at":"2026-05-18T01:53:09Z"},{"alias_kind":"pith_short_12","alias_value":"2TJHBUPCEXTT","created_at":"2026-05-18T12:27:32Z"},{"alias_kind":"pith_short_16","alias_value":"2TJHBUPCEXTTHGYO","created_at":"2026-05-18T12:27:32Z"},{"alias_kind":"pith_short_8","alias_value":"2TJHBUPC","created_at":"2026-05-18T12:27:32Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:2TJHBUPCEXTTHGYOLJJE4VR5W7","target":"record","payload":{"canonical_record":{"source":{"id":"1312.4750","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2013-12-17T12:39:35Z","cross_cats_sorted":[],"title_canon_sha256":"085ee890b35733daa92cfac3c22524174f8e2173f556e715c70a085ea7518224","abstract_canon_sha256":"8fbb4429c467312221e4b1be881df0483ff9baf29eec21eb2cd0e555c667c760"},"schema_version":"1.0"},"canonical_sha256":"d4d270d1e225e7339b0e5a524e563db7de7566ee1b85e7431a18398b75b73682","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:53:09.614219Z","signature_b64":"Wzg0WRwt7OsE6EdFEfPFDYsOiQaAIWlpoEq4N4aXulYU3w6Po66H36UAPw9cBxwTOZ9ZmX5vopSdySqh/XUADw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d4d270d1e225e7339b0e5a524e563db7de7566ee1b85e7431a18398b75b73682","last_reissued_at":"2026-05-18T01:53:09.612917Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:53:09.612917Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1312.4750","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":"2026-05-18T01:53:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jkyiT0sZmweggWjMtEvgEHef0BRt4iBmVZrnPbHJoWTYfNEENaNBBP/9Y3JcgwhVMEcrL33NJbqygpztO4rVBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T23:33:29.080204Z"},"content_sha256":"f128288a635a6cbfdc50a1358265e0ed89a646cad3b7975c60f24ba2bcbc6e06","schema_version":"1.0","event_id":"sha256:f128288a635a6cbfdc50a1358265e0ed89a646cad3b7975c60f24ba2bcbc6e06"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:2TJHBUPCEXTTHGYOLJJE4VR5W7","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Big Free Groups are Almost Free","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Tamer Tlas","submitted_at":"2013-12-17T12:39:35Z","abstract_excerpt":"It is shown that the big free group (the set of countably-long words over a countable alphabet) is almost free, in the sense that any function from the alphabet to a compact topological group factors through a homomorphism. This statement is in fact a simple corollary of the more general result proven below on the extendability of homomorphisms from subgroups (of a certain kind) of the big free group to a compact topological group."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.4750","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":"2026-05-18T01:53:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zWyuMZ8ws++Imu3xbV61DFii9Udy/N430TzPLeAtGVr8tTjIouaMag2re/hx9j7QxZgSbK2sh4vbRf/Z170OAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T23:33:29.080801Z"},"content_sha256":"754affb58e91b78c5bcc72260dbc3bac6727d4fedac3ff246f65a31b4f933f2b","schema_version":"1.0","event_id":"sha256:754affb58e91b78c5bcc72260dbc3bac6727d4fedac3ff246f65a31b4f933f2b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/2TJHBUPCEXTTHGYOLJJE4VR5W7/bundle.json","state_url":"https://pith.science/pith/2TJHBUPCEXTTHGYOLJJE4VR5W7/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/2TJHBUPCEXTTHGYOLJJE4VR5W7/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":"2026-06-10T23:33:29Z","links":{"resolver":"https://pith.science/pith/2TJHBUPCEXTTHGYOLJJE4VR5W7","bundle":"https://pith.science/pith/2TJHBUPCEXTTHGYOLJJE4VR5W7/bundle.json","state":"https://pith.science/pith/2TJHBUPCEXTTHGYOLJJE4VR5W7/state.json","well_known_bundle":"https://pith.science/.well-known/pith/2TJHBUPCEXTTHGYOLJJE4VR5W7/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:2TJHBUPCEXTTHGYOLJJE4VR5W7","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":"8fbb4429c467312221e4b1be881df0483ff9baf29eec21eb2cd0e555c667c760","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2013-12-17T12:39:35Z","title_canon_sha256":"085ee890b35733daa92cfac3c22524174f8e2173f556e715c70a085ea7518224"},"schema_version":"1.0","source":{"id":"1312.4750","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1312.4750","created_at":"2026-05-18T01:53:09Z"},{"alias_kind":"arxiv_version","alias_value":"1312.4750v2","created_at":"2026-05-18T01:53:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1312.4750","created_at":"2026-05-18T01:53:09Z"},{"alias_kind":"pith_short_12","alias_value":"2TJHBUPCEXTT","created_at":"2026-05-18T12:27:32Z"},{"alias_kind":"pith_short_16","alias_value":"2TJHBUPCEXTTHGYO","created_at":"2026-05-18T12:27:32Z"},{"alias_kind":"pith_short_8","alias_value":"2TJHBUPC","created_at":"2026-05-18T12:27:32Z"}],"graph_snapshots":[{"event_id":"sha256:754affb58e91b78c5bcc72260dbc3bac6727d4fedac3ff246f65a31b4f933f2b","target":"graph","created_at":"2026-05-18T01:53:09Z","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":"It is shown that the big free group (the set of countably-long words over a countable alphabet) is almost free, in the sense that any function from the alphabet to a compact topological group factors through a homomorphism. This statement is in fact a simple corollary of the more general result proven below on the extendability of homomorphisms from subgroups (of a certain kind) of the big free group to a compact topological group.","authors_text":"Tamer Tlas","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2013-12-17T12:39:35Z","title":"Big Free Groups are Almost Free"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.4750","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:f128288a635a6cbfdc50a1358265e0ed89a646cad3b7975c60f24ba2bcbc6e06","target":"record","created_at":"2026-05-18T01:53:09Z","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":"8fbb4429c467312221e4b1be881df0483ff9baf29eec21eb2cd0e555c667c760","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2013-12-17T12:39:35Z","title_canon_sha256":"085ee890b35733daa92cfac3c22524174f8e2173f556e715c70a085ea7518224"},"schema_version":"1.0","source":{"id":"1312.4750","kind":"arxiv","version":2}},"canonical_sha256":"d4d270d1e225e7339b0e5a524e563db7de7566ee1b85e7431a18398b75b73682","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d4d270d1e225e7339b0e5a524e563db7de7566ee1b85e7431a18398b75b73682","first_computed_at":"2026-05-18T01:53:09.612917Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:53:09.612917Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Wzg0WRwt7OsE6EdFEfPFDYsOiQaAIWlpoEq4N4aXulYU3w6Po66H36UAPw9cBxwTOZ9ZmX5vopSdySqh/XUADw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:53:09.614219Z","signed_message":"canonical_sha256_bytes"},"source_id":"1312.4750","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f128288a635a6cbfdc50a1358265e0ed89a646cad3b7975c60f24ba2bcbc6e06","sha256:754affb58e91b78c5bcc72260dbc3bac6727d4fedac3ff246f65a31b4f933f2b"],"state_sha256":"663744370193a3f4080af1d662bcc1b93b15ac4bbf05f5dd47f4543a02bf6801"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uPtJ8PCvmzQmY+EkEG350UWK/ezdfNrkzOuhaAbm2juLW/oxlHp9GKr5fOiOw3abWyqwxZKa42K8vCHr5V1uDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-10T23:33:29.084593Z","bundle_sha256":"58b30ae68da1f735cae288c2cdfdeb6c92db09e84a71fd66534c6d8397bf7e5d"}}