{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:L7JOBQOAYPW7FYUNQJJAIOFRAE","short_pith_number":"pith:L7JOBQOA","canonical_record":{"source":{"id":"2607.01879","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2026-07-02T08:34:34Z","cross_cats_sorted":[],"title_canon_sha256":"9dc99eebe9a1dec662611692375a1157800304878df92cdef90cdeb281be7057","abstract_canon_sha256":"f7cb5c8a0342625e20c91e0a139e1af8e12e949645da05905cf4977b94e51c6f"},"schema_version":"1.0"},"canonical_sha256":"5fd2e0c1c0c3edf2e28d82520438b10136340845c4a34d79c6e925b8b0d2c89d","source":{"kind":"arxiv","id":"2607.01879","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.01879","created_at":"2026-07-03T01:17:32Z"},{"alias_kind":"arxiv_version","alias_value":"2607.01879v1","created_at":"2026-07-03T01:17:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.01879","created_at":"2026-07-03T01:17:32Z"},{"alias_kind":"pith_short_12","alias_value":"L7JOBQOAYPW7","created_at":"2026-07-03T01:17:32Z"},{"alias_kind":"pith_short_16","alias_value":"L7JOBQOAYPW7FYUN","created_at":"2026-07-03T01:17:32Z"},{"alias_kind":"pith_short_8","alias_value":"L7JOBQOA","created_at":"2026-07-03T01:17:32Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:L7JOBQOAYPW7FYUNQJJAIOFRAE","target":"record","payload":{"canonical_record":{"source":{"id":"2607.01879","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2026-07-02T08:34:34Z","cross_cats_sorted":[],"title_canon_sha256":"9dc99eebe9a1dec662611692375a1157800304878df92cdef90cdeb281be7057","abstract_canon_sha256":"f7cb5c8a0342625e20c91e0a139e1af8e12e949645da05905cf4977b94e51c6f"},"schema_version":"1.0"},"canonical_sha256":"5fd2e0c1c0c3edf2e28d82520438b10136340845c4a34d79c6e925b8b0d2c89d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-03T01:17:32.389219Z","signature_b64":"ZTRriB0JXzshoC3qfIndtwQzxuy+pqekRNbmFUdIwGgs52Uki0haxbpQKz5h4OKBOxRrVuh9XgaCRkSDTPWBCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5fd2e0c1c0c3edf2e28d82520438b10136340845c4a34d79c6e925b8b0d2c89d","last_reissued_at":"2026-07-03T01:17:32.388807Z","signature_status":"signed_v1","first_computed_at":"2026-07-03T01:17:32.388807Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2607.01879","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-03T01:17:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lG5wkCT7Xut+c9iBuHNGZg9wJJocIFArCl0aj09GwbQTNnfNASmayOK5HoU6WDzefjIiTzkBoZKF8RqxEcSRAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-06T04:45:57.059598Z"},"content_sha256":"806c3d72b564fa89b489e43225f6cd50db01526d554c6e52566d3c75d6a5236b","schema_version":"1.0","event_id":"sha256:806c3d72b564fa89b489e43225f6cd50db01526d554c6e52566d3c75d6a5236b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:L7JOBQOAYPW7FYUNQJJAIOFRAE","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Exponential growth rates of even Coxeter groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Michelle Bucher, V\\'era Bossart","submitted_at":"2026-07-02T08:34:34Z","abstract_excerpt":"Let $W$ be an even Coxeter group. We prove that among all Coxeter systems generating $W$ the unique even Coxeter system realizes the minimal exponential growth. Our proof relies on comparing the exponential growth rates in the explicit algorithm of Mihalik which from any Coxeter system of an even Coxeter group eventually produces the unique even one. The main new ingredient is that blow downs along pseudo-transpositions do not increase the exponential growth rate."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.01879","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2607.01879/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-03T01:17:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"flB590ppqvEPc9CA0OGBfzvMSRbtfDk0OVnEmLa58B9owHoS560ge3gUcKPGdcRhIcBxSHoBnD+v2cX4m5YfDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-06T04:45:57.060827Z"},"content_sha256":"e8f13050a291e6ebcc5682579c0f7641f77c96437030e9ee7d235801b8b3d843","schema_version":"1.0","event_id":"sha256:e8f13050a291e6ebcc5682579c0f7641f77c96437030e9ee7d235801b8b3d843"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/L7JOBQOAYPW7FYUNQJJAIOFRAE/bundle.json","state_url":"https://pith.science/pith/L7JOBQOAYPW7FYUNQJJAIOFRAE/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/L7JOBQOAYPW7FYUNQJJAIOFRAE/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":"2026-08-06T04:45:57Z","links":{"resolver":"https://pith.science/pith/L7JOBQOAYPW7FYUNQJJAIOFRAE","bundle":"https://pith.science/pith/L7JOBQOAYPW7FYUNQJJAIOFRAE/bundle.json","state":"https://pith.science/pith/L7JOBQOAYPW7FYUNQJJAIOFRAE/state.json","well_known_bundle":"https://pith.science/.well-known/pith/L7JOBQOAYPW7FYUNQJJAIOFRAE/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:L7JOBQOAYPW7FYUNQJJAIOFRAE","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":"f7cb5c8a0342625e20c91e0a139e1af8e12e949645da05905cf4977b94e51c6f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2026-07-02T08:34:34Z","title_canon_sha256":"9dc99eebe9a1dec662611692375a1157800304878df92cdef90cdeb281be7057"},"schema_version":"1.0","source":{"id":"2607.01879","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.01879","created_at":"2026-07-03T01:17:32Z"},{"alias_kind":"arxiv_version","alias_value":"2607.01879v1","created_at":"2026-07-03T01:17:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.01879","created_at":"2026-07-03T01:17:32Z"},{"alias_kind":"pith_short_12","alias_value":"L7JOBQOAYPW7","created_at":"2026-07-03T01:17:32Z"},{"alias_kind":"pith_short_16","alias_value":"L7JOBQOAYPW7FYUN","created_at":"2026-07-03T01:17:32Z"},{"alias_kind":"pith_short_8","alias_value":"L7JOBQOA","created_at":"2026-07-03T01:17:32Z"}],"graph_snapshots":[{"event_id":"sha256:e8f13050a291e6ebcc5682579c0f7641f77c96437030e9ee7d235801b8b3d843","target":"graph","created_at":"2026-07-03T01:17:32Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2607.01879/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Let $W$ be an even Coxeter group. We prove that among all Coxeter systems generating $W$ the unique even Coxeter system realizes the minimal exponential growth. Our proof relies on comparing the exponential growth rates in the explicit algorithm of Mihalik which from any Coxeter system of an even Coxeter group eventually produces the unique even one. The main new ingredient is that blow downs along pseudo-transpositions do not increase the exponential growth rate.","authors_text":"Michelle Bucher, V\\'era Bossart","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2026-07-02T08:34:34Z","title":"Exponential growth rates of even Coxeter groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.01879","kind":"arxiv","version":1},"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":"sha256:806c3d72b564fa89b489e43225f6cd50db01526d554c6e52566d3c75d6a5236b","target":"record","created_at":"2026-07-03T01:17:32Z","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":"f7cb5c8a0342625e20c91e0a139e1af8e12e949645da05905cf4977b94e51c6f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2026-07-02T08:34:34Z","title_canon_sha256":"9dc99eebe9a1dec662611692375a1157800304878df92cdef90cdeb281be7057"},"schema_version":"1.0","source":{"id":"2607.01879","kind":"arxiv","version":1}},"canonical_sha256":"5fd2e0c1c0c3edf2e28d82520438b10136340845c4a34d79c6e925b8b0d2c89d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5fd2e0c1c0c3edf2e28d82520438b10136340845c4a34d79c6e925b8b0d2c89d","first_computed_at":"2026-07-03T01:17:32.388807Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-03T01:17:32.388807Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ZTRriB0JXzshoC3qfIndtwQzxuy+pqekRNbmFUdIwGgs52Uki0haxbpQKz5h4OKBOxRrVuh9XgaCRkSDTPWBCg==","signature_status":"signed_v1","signed_at":"2026-07-03T01:17:32.389219Z","signed_message":"canonical_sha256_bytes"},"source_id":"2607.01879","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:806c3d72b564fa89b489e43225f6cd50db01526d554c6e52566d3c75d6a5236b","sha256:e8f13050a291e6ebcc5682579c0f7641f77c96437030e9ee7d235801b8b3d843"],"state_sha256":"b2190ee0aff87878858a566fc1227a056bcc360270d10e2d5158fd131f7a4cbb"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6L8aJ6WObFY28WaJtC+UIcLvDLvztK04DqBl1UJKM1WrM28tmp17Yyq+q+uHi5wn5bCTGGWTWbl7QGsydfRsAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-06T04:45:57.071540Z","bundle_sha256":"945d8f729e06c35db9c990ae1cc1e48c44fc0449ee382f0c9d2296d7a753c015"}}