{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2009:QJXKXVUT7BLXIK52ARF4XT2KLM","short_pith_number":"pith:QJXKXVUT","canonical_record":{"source":{"id":"0908.1268","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2009-08-10T04:14:54Z","cross_cats_sorted":[],"title_canon_sha256":"020949dc3043dd2d33628873c1b65322484760d4ca71a9e231f7dff9ee774104","abstract_canon_sha256":"6a84433375caa212d54b2b63bd5547c91d82d2dcb17c8659277302be9dbf3b08"},"schema_version":"1.0"},"canonical_sha256":"826eabd693f857742bba044bcbcf4a5b3b3aed5d7e0a0bd25580a44c3e3ebcf1","source":{"kind":"arxiv","id":"0908.1268","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0908.1268","created_at":"2026-05-18T04:40:46Z"},{"alias_kind":"arxiv_version","alias_value":"0908.1268v2","created_at":"2026-05-18T04:40:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0908.1268","created_at":"2026-05-18T04:40:46Z"},{"alias_kind":"pith_short_12","alias_value":"QJXKXVUT7BLX","created_at":"2026-05-18T12:26:01Z"},{"alias_kind":"pith_short_16","alias_value":"QJXKXVUT7BLXIK52","created_at":"2026-05-18T12:26:01Z"},{"alias_kind":"pith_short_8","alias_value":"QJXKXVUT","created_at":"2026-05-18T12:26:01Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2009:QJXKXVUT7BLXIK52ARF4XT2KLM","target":"record","payload":{"canonical_record":{"source":{"id":"0908.1268","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2009-08-10T04:14:54Z","cross_cats_sorted":[],"title_canon_sha256":"020949dc3043dd2d33628873c1b65322484760d4ca71a9e231f7dff9ee774104","abstract_canon_sha256":"6a84433375caa212d54b2b63bd5547c91d82d2dcb17c8659277302be9dbf3b08"},"schema_version":"1.0"},"canonical_sha256":"826eabd693f857742bba044bcbcf4a5b3b3aed5d7e0a0bd25580a44c3e3ebcf1","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:40:46.468249Z","signature_b64":"eT3ilBz1baB+/II3YtT9tbjIasTA23MwOo7nH3GnU9kG6n8Jr+nktWdiAQlU4KUnCbqTz6vFOE0YN2DZ4z7ODA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"826eabd693f857742bba044bcbcf4a5b3b3aed5d7e0a0bd25580a44c3e3ebcf1","last_reissued_at":"2026-05-18T04:40:46.467609Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:40:46.467609Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0908.1268","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":"2026-05-18T04:40:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SOHOkZwjc6awi1Cvi5VJti9iHJvFFvUr3KjrOiIJCq3gygDYZElAzc7I44XSHWgfTXKvpZ0TKcZR4aTky51AAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T17:11:05.036478Z"},"content_sha256":"d2bccd76c1cf298fabe55ae47565071b1955e6c6e921331412f67104380ba27c","schema_version":"1.0","event_id":"sha256:d2bccd76c1cf298fabe55ae47565071b1955e6c6e921331412f67104380ba27c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2009:QJXKXVUT7BLXIK52ARF4XT2KLM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Free limits of Thompson's group $F$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Azer Akhmedov, Jennifer Taback, Melanie Stein","submitted_at":"2009-08-10T04:14:54Z","abstract_excerpt":"We produce a sequence of markings $S_k$ of Thompson's group $F$ within the space ${\\mathcal G}_n$ of all marked $n$-generator groups so that the sequence $(F,S_k)$ converges to the free group on $n$ generators, for $n \\geq 3$. In addition, we give presentations for the limits of some other natural (convergent) sequences of markings to consider on $F$ within ${\\mathcal G}_3$, including $(F,\\{x_0,x_1,x_n\\})$ and $(F,\\{x_0,x_1,x_0^n\\})$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0908.1268","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":"2026-05-18T04:40:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pbYgzUsuptjQNhrTkvQOT7nzXwC7riQ6FMNdiHnsD7AqexiaiwDhkv1vZHrZGaZve7zpRGejEC7RN9amhJeLAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T17:11:05.037099Z"},"content_sha256":"92748558cad67e1b9ba27a5b0d8d3f7228d2cdf0e84c450a9a864be6f7b251f4","schema_version":"1.0","event_id":"sha256:92748558cad67e1b9ba27a5b0d8d3f7228d2cdf0e84c450a9a864be6f7b251f4"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QJXKXVUT7BLXIK52ARF4XT2KLM/bundle.json","state_url":"https://pith.science/pith/QJXKXVUT7BLXIK52ARF4XT2KLM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QJXKXVUT7BLXIK52ARF4XT2KLM/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":"2026-06-22T17:11:05Z","links":{"resolver":"https://pith.science/pith/QJXKXVUT7BLXIK52ARF4XT2KLM","bundle":"https://pith.science/pith/QJXKXVUT7BLXIK52ARF4XT2KLM/bundle.json","state":"https://pith.science/pith/QJXKXVUT7BLXIK52ARF4XT2KLM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QJXKXVUT7BLXIK52ARF4XT2KLM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:QJXKXVUT7BLXIK52ARF4XT2KLM","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":"6a84433375caa212d54b2b63bd5547c91d82d2dcb17c8659277302be9dbf3b08","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2009-08-10T04:14:54Z","title_canon_sha256":"020949dc3043dd2d33628873c1b65322484760d4ca71a9e231f7dff9ee774104"},"schema_version":"1.0","source":{"id":"0908.1268","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0908.1268","created_at":"2026-05-18T04:40:46Z"},{"alias_kind":"arxiv_version","alias_value":"0908.1268v2","created_at":"2026-05-18T04:40:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0908.1268","created_at":"2026-05-18T04:40:46Z"},{"alias_kind":"pith_short_12","alias_value":"QJXKXVUT7BLX","created_at":"2026-05-18T12:26:01Z"},{"alias_kind":"pith_short_16","alias_value":"QJXKXVUT7BLXIK52","created_at":"2026-05-18T12:26:01Z"},{"alias_kind":"pith_short_8","alias_value":"QJXKXVUT","created_at":"2026-05-18T12:26:01Z"}],"graph_snapshots":[{"event_id":"sha256:92748558cad67e1b9ba27a5b0d8d3f7228d2cdf0e84c450a9a864be6f7b251f4","target":"graph","created_at":"2026-05-18T04:40:46Z","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 produce a sequence of markings $S_k$ of Thompson's group $F$ within the space ${\\mathcal G}_n$ of all marked $n$-generator groups so that the sequence $(F,S_k)$ converges to the free group on $n$ generators, for $n \\geq 3$. In addition, we give presentations for the limits of some other natural (convergent) sequences of markings to consider on $F$ within ${\\mathcal G}_3$, including $(F,\\{x_0,x_1,x_n\\})$ and $(F,\\{x_0,x_1,x_0^n\\})$.","authors_text":"Azer Akhmedov, Jennifer Taback, Melanie Stein","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2009-08-10T04:14:54Z","title":"Free limits of Thompson's group $F$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0908.1268","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:d2bccd76c1cf298fabe55ae47565071b1955e6c6e921331412f67104380ba27c","target":"record","created_at":"2026-05-18T04:40:46Z","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":"6a84433375caa212d54b2b63bd5547c91d82d2dcb17c8659277302be9dbf3b08","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2009-08-10T04:14:54Z","title_canon_sha256":"020949dc3043dd2d33628873c1b65322484760d4ca71a9e231f7dff9ee774104"},"schema_version":"1.0","source":{"id":"0908.1268","kind":"arxiv","version":2}},"canonical_sha256":"826eabd693f857742bba044bcbcf4a5b3b3aed5d7e0a0bd25580a44c3e3ebcf1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"826eabd693f857742bba044bcbcf4a5b3b3aed5d7e0a0bd25580a44c3e3ebcf1","first_computed_at":"2026-05-18T04:40:46.467609Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:40:46.467609Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"eT3ilBz1baB+/II3YtT9tbjIasTA23MwOo7nH3GnU9kG6n8Jr+nktWdiAQlU4KUnCbqTz6vFOE0YN2DZ4z7ODA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:40:46.468249Z","signed_message":"canonical_sha256_bytes"},"source_id":"0908.1268","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d2bccd76c1cf298fabe55ae47565071b1955e6c6e921331412f67104380ba27c","sha256:92748558cad67e1b9ba27a5b0d8d3f7228d2cdf0e84c450a9a864be6f7b251f4"],"state_sha256":"8eba0a6b200f02b85ddbac80fc15e4d41cfac97c791267a5b1cb95ef8da12226"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VTdH1VHU7CeoEu53/AIBvzHsdI+TbocXFblJwzgSwYtLbs6A00u+c2VMQ851Ow0Erij7fhIVTgEKTvk+XUmVDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-22T17:11:05.040132Z","bundle_sha256":"c8cf6cd8b29a96f61f117e8f5e19713475d3e915cf009205368c30cac0476e05"}}