{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:HLPYO7L754W75CDDNJC7ORQ3HT","short_pith_number":"pith:HLPYO7L7","canonical_record":{"source":{"id":"1511.04148","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2015-11-13T03:27:28Z","cross_cats_sorted":[],"title_canon_sha256":"1a12f51bfb92c8b29ef30b58f4c9e32a720645bde866088b5060ae03bb71fe41","abstract_canon_sha256":"0d0ab7c0517c316eb2647a25d2fa71a2b5fa0af97c38f8704bab592ecd504a0d"},"schema_version":"1.0"},"canonical_sha256":"3adf877d7fef2dfe88636a45f7461b3cf78010e4783673b4621c1c22695b2245","source":{"kind":"arxiv","id":"1511.04148","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1511.04148","created_at":"2026-05-18T01:26:31Z"},{"alias_kind":"arxiv_version","alias_value":"1511.04148v2","created_at":"2026-05-18T01:26:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1511.04148","created_at":"2026-05-18T01:26:31Z"},{"alias_kind":"pith_short_12","alias_value":"HLPYO7L754W7","created_at":"2026-05-18T12:29:25Z"},{"alias_kind":"pith_short_16","alias_value":"HLPYO7L754W75CDD","created_at":"2026-05-18T12:29:25Z"},{"alias_kind":"pith_short_8","alias_value":"HLPYO7L7","created_at":"2026-05-18T12:29:25Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:HLPYO7L754W75CDDNJC7ORQ3HT","target":"record","payload":{"canonical_record":{"source":{"id":"1511.04148","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2015-11-13T03:27:28Z","cross_cats_sorted":[],"title_canon_sha256":"1a12f51bfb92c8b29ef30b58f4c9e32a720645bde866088b5060ae03bb71fe41","abstract_canon_sha256":"0d0ab7c0517c316eb2647a25d2fa71a2b5fa0af97c38f8704bab592ecd504a0d"},"schema_version":"1.0"},"canonical_sha256":"3adf877d7fef2dfe88636a45f7461b3cf78010e4783673b4621c1c22695b2245","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:26:31.018811Z","signature_b64":"D73HkjyOFp15c9cF7YRenpIwoMzTwEXq2WEQgXy6woiOHFacSxP7u9wqFQWBKDImw/iANge9s+a8pcuiAzkFBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3adf877d7fef2dfe88636a45f7461b3cf78010e4783673b4621c1c22695b2245","last_reissued_at":"2026-05-18T01:26:31.018120Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:26:31.018120Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1511.04148","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":"2026-05-18T01:26:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fRIJ2xObWCYyOs7nCfRKyJMuRmNDnQzbRwan+vxJ1Aumdh/llibReWQ0Wo24HHPFPqIWR43X6Hvd+xcv0NjLAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T01:15:35.618852Z"},"content_sha256":"b4bb06ea1c262ea5ec8834d3c411f8b2678c669ab58dc4a69453861e5726d2a8","schema_version":"1.0","event_id":"sha256:b4bb06ea1c262ea5ec8834d3c411f8b2678c669ab58dc4a69453861e5726d2a8"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:HLPYO7L754W75CDDNJC7ORQ3HT","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Dehn function of Richard Thompson's group $T$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Junhuai Zhang, Kun Wang, Zhu-Jun Zheng","submitted_at":"2015-11-13T03:27:28Z","abstract_excerpt":"V.S.Guba had proved that the R.Thompson group $T$ satisfies polynomial isoperimetric inequality and $\\Phi_T(n)\\preceq n^7$, where $\\Phi_T$ is the Dehn function of group $T$. In this paper, we show that $\\Phi_T(n)\\preceq n^5$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.04148","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":"2026-05-18T01:26:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MM3oOonGIgY2dezwrT6K97FDwVfKfqvJ/T29/zvtdeMYIOPn9TwHmxSJXVF2/F4n6VApdFzLqCL12ixiAkszBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T01:15:35.619201Z"},"content_sha256":"bd13bee119ca8479c25c1dac19555aca02db0f5de0a29cdd0e9b1394ef6586d7","schema_version":"1.0","event_id":"sha256:bd13bee119ca8479c25c1dac19555aca02db0f5de0a29cdd0e9b1394ef6586d7"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HLPYO7L754W75CDDNJC7ORQ3HT/bundle.json","state_url":"https://pith.science/pith/HLPYO7L754W75CDDNJC7ORQ3HT/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HLPYO7L754W75CDDNJC7ORQ3HT/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":"2026-06-02T01:15:35Z","links":{"resolver":"https://pith.science/pith/HLPYO7L754W75CDDNJC7ORQ3HT","bundle":"https://pith.science/pith/HLPYO7L754W75CDDNJC7ORQ3HT/bundle.json","state":"https://pith.science/pith/HLPYO7L754W75CDDNJC7ORQ3HT/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HLPYO7L754W75CDDNJC7ORQ3HT/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:HLPYO7L754W75CDDNJC7ORQ3HT","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":"0d0ab7c0517c316eb2647a25d2fa71a2b5fa0af97c38f8704bab592ecd504a0d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2015-11-13T03:27:28Z","title_canon_sha256":"1a12f51bfb92c8b29ef30b58f4c9e32a720645bde866088b5060ae03bb71fe41"},"schema_version":"1.0","source":{"id":"1511.04148","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1511.04148","created_at":"2026-05-18T01:26:31Z"},{"alias_kind":"arxiv_version","alias_value":"1511.04148v2","created_at":"2026-05-18T01:26:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1511.04148","created_at":"2026-05-18T01:26:31Z"},{"alias_kind":"pith_short_12","alias_value":"HLPYO7L754W7","created_at":"2026-05-18T12:29:25Z"},{"alias_kind":"pith_short_16","alias_value":"HLPYO7L754W75CDD","created_at":"2026-05-18T12:29:25Z"},{"alias_kind":"pith_short_8","alias_value":"HLPYO7L7","created_at":"2026-05-18T12:29:25Z"}],"graph_snapshots":[{"event_id":"sha256:bd13bee119ca8479c25c1dac19555aca02db0f5de0a29cdd0e9b1394ef6586d7","target":"graph","created_at":"2026-05-18T01:26:31Z","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":"V.S.Guba had proved that the R.Thompson group $T$ satisfies polynomial isoperimetric inequality and $\\Phi_T(n)\\preceq n^7$, where $\\Phi_T$ is the Dehn function of group $T$. In this paper, we show that $\\Phi_T(n)\\preceq n^5$.","authors_text":"Junhuai Zhang, Kun Wang, Zhu-Jun Zheng","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2015-11-13T03:27:28Z","title":"The Dehn function of Richard Thompson's group $T$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.04148","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:b4bb06ea1c262ea5ec8834d3c411f8b2678c669ab58dc4a69453861e5726d2a8","target":"record","created_at":"2026-05-18T01:26:31Z","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":"0d0ab7c0517c316eb2647a25d2fa71a2b5fa0af97c38f8704bab592ecd504a0d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2015-11-13T03:27:28Z","title_canon_sha256":"1a12f51bfb92c8b29ef30b58f4c9e32a720645bde866088b5060ae03bb71fe41"},"schema_version":"1.0","source":{"id":"1511.04148","kind":"arxiv","version":2}},"canonical_sha256":"3adf877d7fef2dfe88636a45f7461b3cf78010e4783673b4621c1c22695b2245","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3adf877d7fef2dfe88636a45f7461b3cf78010e4783673b4621c1c22695b2245","first_computed_at":"2026-05-18T01:26:31.018120Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:26:31.018120Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"D73HkjyOFp15c9cF7YRenpIwoMzTwEXq2WEQgXy6woiOHFacSxP7u9wqFQWBKDImw/iANge9s+a8pcuiAzkFBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:26:31.018811Z","signed_message":"canonical_sha256_bytes"},"source_id":"1511.04148","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b4bb06ea1c262ea5ec8834d3c411f8b2678c669ab58dc4a69453861e5726d2a8","sha256:bd13bee119ca8479c25c1dac19555aca02db0f5de0a29cdd0e9b1394ef6586d7"],"state_sha256":"0844ad91653a2305d08458a6325b11982935b7ddc46bb3959aab86855aa70582"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EPeI2JnxGT4SCX4S9RLBppAxyb5r7kPnfOOIDRlnTwVDwsJQGKar+EQm6WOzrg4gqEdOF6D2nrOkJNd7K5xDCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T01:15:35.621133Z","bundle_sha256":"679a7378baf70dde538c5aa1ca08a756df80d7fac5f54f517c3a1f079be84772"}}