{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:2TSVCODUWXGNTT5P4IOG2CZ6YN","short_pith_number":"pith:2TSVCODU","canonical_record":{"source":{"id":"1607.00052","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2016-06-30T21:28:27Z","cross_cats_sorted":[],"title_canon_sha256":"4f74498bdc3691d1eee831c4ec1658f828c0b6ef3b5de33f378b3fb3dfc2ac3e","abstract_canon_sha256":"da24fdd10f10d45392e92339128d4e069f2387d2b1191d1c7c430566564c0fe5"},"schema_version":"1.0"},"canonical_sha256":"d4e5513874b5ccd9cfafe21c6d0b3ec37ca10114dbfac2e38654be2d330f71d1","source":{"kind":"arxiv","id":"1607.00052","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1607.00052","created_at":"2026-05-17T23:45:00Z"},{"alias_kind":"arxiv_version","alias_value":"1607.00052v3","created_at":"2026-05-17T23:45:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1607.00052","created_at":"2026-05-17T23:45:00Z"},{"alias_kind":"pith_short_12","alias_value":"2TSVCODUWXGN","created_at":"2026-05-18T12:29:55Z"},{"alias_kind":"pith_short_16","alias_value":"2TSVCODUWXGNTT5P","created_at":"2026-05-18T12:29:55Z"},{"alias_kind":"pith_short_8","alias_value":"2TSVCODU","created_at":"2026-05-18T12:29:55Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:2TSVCODUWXGNTT5P4IOG2CZ6YN","target":"record","payload":{"canonical_record":{"source":{"id":"1607.00052","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2016-06-30T21:28:27Z","cross_cats_sorted":[],"title_canon_sha256":"4f74498bdc3691d1eee831c4ec1658f828c0b6ef3b5de33f378b3fb3dfc2ac3e","abstract_canon_sha256":"da24fdd10f10d45392e92339128d4e069f2387d2b1191d1c7c430566564c0fe5"},"schema_version":"1.0"},"canonical_sha256":"d4e5513874b5ccd9cfafe21c6d0b3ec37ca10114dbfac2e38654be2d330f71d1","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:45:00.422056Z","signature_b64":"X9aWkp3qP+OhHzB1R1npWlZPRK9Vn/HSt+gOB8yguBGJIsHhqx6pJ4XNqln98NHFZe0Kes+/LRSbKq6f1ralDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d4e5513874b5ccd9cfafe21c6d0b3ec37ca10114dbfac2e38654be2d330f71d1","last_reissued_at":"2026-05-17T23:45:00.421401Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:45:00.421401Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1607.00052","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:45:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dPnBnsVvUtwnNvxZGPhiC99IhYpMATY6JEXkKLmlpg9zrkpcsMC7RNgww+QTa254acE7OZkYY0u7fg5Q8EZ+AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T11:28:35.785329Z"},"content_sha256":"b34f1813a4acfd2d1648d1816d838831ec0ea3be15975a516604347255477bac","schema_version":"1.0","event_id":"sha256:b34f1813a4acfd2d1648d1816d838831ec0ea3be15975a516604347255477bac"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:2TSVCODUWXGNTT5P4IOG2CZ6YN","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Uniform exponential growth for CAT(0) square complexes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Aditi Kar, Michah Sageev","submitted_at":"2016-06-30T21:28:27Z","abstract_excerpt":"In this paper we start the inquiry into proving uniform exponential growth in the context of groups acting on CAT(0) cube complexes. We address free group actions on CAT(0) square complexes and prove a more general statement. This says that if $F$ is a finite collection of hyperbolic automorphisms of a CAT(0) square complex $X$, then either there exists a pair of words of length at most 10 in $F$ which freely generate a free semigroup, or all elements of $F$ stabilize a flat (of dimension 1 or 2 in $X$). As a corollary, we obtain a lower bound for the growth constant, $\\sqrt[10]{2}$, which is "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.00052","kind":"arxiv","version":3},"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":"2026-05-17T23:45:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"z48HakudSHDyXsKJe3O7sk1KmpDzyQa8u0TpDm4OGzn6SryEgLNJgIUys1llSXkLflYdPjYIF4dluMmP7WMiAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T11:28:35.785689Z"},"content_sha256":"97669c3d33df64721640a5efe08e5769a5a0dd0bb72e3252c1a36227bd375fd9","schema_version":"1.0","event_id":"sha256:97669c3d33df64721640a5efe08e5769a5a0dd0bb72e3252c1a36227bd375fd9"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/2TSVCODUWXGNTT5P4IOG2CZ6YN/bundle.json","state_url":"https://pith.science/pith/2TSVCODUWXGNTT5P4IOG2CZ6YN/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/2TSVCODUWXGNTT5P4IOG2CZ6YN/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":"2026-05-28T11:28:35Z","links":{"resolver":"https://pith.science/pith/2TSVCODUWXGNTT5P4IOG2CZ6YN","bundle":"https://pith.science/pith/2TSVCODUWXGNTT5P4IOG2CZ6YN/bundle.json","state":"https://pith.science/pith/2TSVCODUWXGNTT5P4IOG2CZ6YN/state.json","well_known_bundle":"https://pith.science/.well-known/pith/2TSVCODUWXGNTT5P4IOG2CZ6YN/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:2TSVCODUWXGNTT5P4IOG2CZ6YN","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":"da24fdd10f10d45392e92339128d4e069f2387d2b1191d1c7c430566564c0fe5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2016-06-30T21:28:27Z","title_canon_sha256":"4f74498bdc3691d1eee831c4ec1658f828c0b6ef3b5de33f378b3fb3dfc2ac3e"},"schema_version":"1.0","source":{"id":"1607.00052","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1607.00052","created_at":"2026-05-17T23:45:00Z"},{"alias_kind":"arxiv_version","alias_value":"1607.00052v3","created_at":"2026-05-17T23:45:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1607.00052","created_at":"2026-05-17T23:45:00Z"},{"alias_kind":"pith_short_12","alias_value":"2TSVCODUWXGN","created_at":"2026-05-18T12:29:55Z"},{"alias_kind":"pith_short_16","alias_value":"2TSVCODUWXGNTT5P","created_at":"2026-05-18T12:29:55Z"},{"alias_kind":"pith_short_8","alias_value":"2TSVCODU","created_at":"2026-05-18T12:29:55Z"}],"graph_snapshots":[{"event_id":"sha256:97669c3d33df64721640a5efe08e5769a5a0dd0bb72e3252c1a36227bd375fd9","target":"graph","created_at":"2026-05-17T23:45:00Z","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":"In this paper we start the inquiry into proving uniform exponential growth in the context of groups acting on CAT(0) cube complexes. We address free group actions on CAT(0) square complexes and prove a more general statement. This says that if $F$ is a finite collection of hyperbolic automorphisms of a CAT(0) square complex $X$, then either there exists a pair of words of length at most 10 in $F$ which freely generate a free semigroup, or all elements of $F$ stabilize a flat (of dimension 1 or 2 in $X$). As a corollary, we obtain a lower bound for the growth constant, $\\sqrt[10]{2}$, which is ","authors_text":"Aditi Kar, Michah Sageev","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2016-06-30T21:28:27Z","title":"Uniform exponential growth for CAT(0) square complexes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.00052","kind":"arxiv","version":3},"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:b34f1813a4acfd2d1648d1816d838831ec0ea3be15975a516604347255477bac","target":"record","created_at":"2026-05-17T23:45:00Z","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":"da24fdd10f10d45392e92339128d4e069f2387d2b1191d1c7c430566564c0fe5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2016-06-30T21:28:27Z","title_canon_sha256":"4f74498bdc3691d1eee831c4ec1658f828c0b6ef3b5de33f378b3fb3dfc2ac3e"},"schema_version":"1.0","source":{"id":"1607.00052","kind":"arxiv","version":3}},"canonical_sha256":"d4e5513874b5ccd9cfafe21c6d0b3ec37ca10114dbfac2e38654be2d330f71d1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d4e5513874b5ccd9cfafe21c6d0b3ec37ca10114dbfac2e38654be2d330f71d1","first_computed_at":"2026-05-17T23:45:00.421401Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:45:00.421401Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"X9aWkp3qP+OhHzB1R1npWlZPRK9Vn/HSt+gOB8yguBGJIsHhqx6pJ4XNqln98NHFZe0Kes+/LRSbKq6f1ralDw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:45:00.422056Z","signed_message":"canonical_sha256_bytes"},"source_id":"1607.00052","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b34f1813a4acfd2d1648d1816d838831ec0ea3be15975a516604347255477bac","sha256:97669c3d33df64721640a5efe08e5769a5a0dd0bb72e3252c1a36227bd375fd9"],"state_sha256":"16a069658b1052308f1404905665c83dd931aae99bf8319f7619375f32877f19"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uviVn8vwZbKoUsVHIs7TUSF8XdgTZtMVlMguRSvWcLZeR8kqFYPAOt6lREIxG8yaiLB/v9Nua/PD3HbZ1cm4BA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T11:28:35.787614Z","bundle_sha256":"9753aafb8f945def4fc1fd8573e1baf7f9149eef43756c2c15d94b470a20ca2d"}}