{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:LSVSRZDY23KXUCEJKSW73WG4SW","short_pith_number":"pith:LSVSRZDY","canonical_record":{"source":{"id":"1501.03419","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-01-14T17:32:00Z","cross_cats_sorted":[],"title_canon_sha256":"0ba843f4c4c68a40caa825341a439868d4a35da9dfdd37f53dc67aed5bd2e63a","abstract_canon_sha256":"796c153d00bfca27b5fbdcc1f159538bbc0d31b739c0ddf2c0b66b5f1dca8697"},"schema_version":"1.0"},"canonical_sha256":"5cab28e478d6d57a088954adfdd8dc959da5f29e81edc013fb5cdcd37ba900a2","source":{"kind":"arxiv","id":"1501.03419","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1501.03419","created_at":"2026-05-18T00:51:03Z"},{"alias_kind":"arxiv_version","alias_value":"1501.03419v4","created_at":"2026-05-18T00:51:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1501.03419","created_at":"2026-05-18T00:51:03Z"},{"alias_kind":"pith_short_12","alias_value":"LSVSRZDY23KX","created_at":"2026-05-18T12:29:29Z"},{"alias_kind":"pith_short_16","alias_value":"LSVSRZDY23KXUCEJ","created_at":"2026-05-18T12:29:29Z"},{"alias_kind":"pith_short_8","alias_value":"LSVSRZDY","created_at":"2026-05-18T12:29:29Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:LSVSRZDY23KXUCEJKSW73WG4SW","target":"record","payload":{"canonical_record":{"source":{"id":"1501.03419","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-01-14T17:32:00Z","cross_cats_sorted":[],"title_canon_sha256":"0ba843f4c4c68a40caa825341a439868d4a35da9dfdd37f53dc67aed5bd2e63a","abstract_canon_sha256":"796c153d00bfca27b5fbdcc1f159538bbc0d31b739c0ddf2c0b66b5f1dca8697"},"schema_version":"1.0"},"canonical_sha256":"5cab28e478d6d57a088954adfdd8dc959da5f29e81edc013fb5cdcd37ba900a2","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:51:03.459341Z","signature_b64":"thUx8j7t4dDKfbzgWuTXXXYR7cEKH21MHDPFfVR+yxVSqIQAcDMNPSEBsopYG98NsyD/AnHBM7gVGcFaO6iTBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5cab28e478d6d57a088954adfdd8dc959da5f29e81edc013fb5cdcd37ba900a2","last_reissued_at":"2026-05-18T00:51:03.458955Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:51:03.458955Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1501.03419","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:51:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"n7rBVyIME2h7jtoxVSI8x8Ki7JHvjoegZHz7kwvBBE08vCQSd1mXAMu1mEn05fM71WQXu/F5a2uTGwFIdnXNDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T14:07:25.455889Z"},"content_sha256":"36ae462d0b2be654d02d23af3e676ca14e673a12ece44b88fdd60bca0aa05590","schema_version":"1.0","event_id":"sha256:36ae462d0b2be654d02d23af3e676ca14e673a12ece44b88fdd60bca0aa05590"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:LSVSRZDY23KXUCEJKSW73WG4SW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Joint spectral radius, Sturmian measures, and the finiteness conjecture","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Mark Pollicott, Oliver Jenkinson","submitted_at":"2015-01-14T17:32:00Z","abstract_excerpt":"The joint spectral radius of a pair of 2x2 real matrices $(A_0,A_1)\\in M_2(\\mathbb{R})^2$ is defined to be $r(A_0,A_1)= \\limsup_{n\\to\\infty} \\max \\{\\|A_{i_1}...A_{i_n}\\|^{1/n}: i_j\\in\\{0,1\\}\\}$, the optimal growth rate of the norm of products of these matrices. The Lagarias-Wang finiteness conjecture, asserting that $r(A_0,A_1)$ is always the nth root of the spectral radius of some length-n product $A_{i_1}...A_{i_n}$, has been refuted by Bousch & Mairesse, with subsequent counterexamples presented by Blondel, Theys & Vladimirov; Kozyakin; Hare, Morris, Sidorov & Theys. In this article we intr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.03419","kind":"arxiv","version":4},"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":"2026-05-18T00:51:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BjtChspKvXmpBXUCo5Hlp+JrrsGUwFRUApfIzseH14LsRInIUsAc1CEtBQ+qzPxlw2aVOMog/5byxZB29LhRBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T14:07:25.456239Z"},"content_sha256":"1962a38dfb15368a1e5552dce7476add8e909771dd6768c8a80ad586e64924f5","schema_version":"1.0","event_id":"sha256:1962a38dfb15368a1e5552dce7476add8e909771dd6768c8a80ad586e64924f5"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/LSVSRZDY23KXUCEJKSW73WG4SW/bundle.json","state_url":"https://pith.science/pith/LSVSRZDY23KXUCEJKSW73WG4SW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/LSVSRZDY23KXUCEJKSW73WG4SW/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":"2026-06-11T14:07:25Z","links":{"resolver":"https://pith.science/pith/LSVSRZDY23KXUCEJKSW73WG4SW","bundle":"https://pith.science/pith/LSVSRZDY23KXUCEJKSW73WG4SW/bundle.json","state":"https://pith.science/pith/LSVSRZDY23KXUCEJKSW73WG4SW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/LSVSRZDY23KXUCEJKSW73WG4SW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:LSVSRZDY23KXUCEJKSW73WG4SW","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":"796c153d00bfca27b5fbdcc1f159538bbc0d31b739c0ddf2c0b66b5f1dca8697","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-01-14T17:32:00Z","title_canon_sha256":"0ba843f4c4c68a40caa825341a439868d4a35da9dfdd37f53dc67aed5bd2e63a"},"schema_version":"1.0","source":{"id":"1501.03419","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1501.03419","created_at":"2026-05-18T00:51:03Z"},{"alias_kind":"arxiv_version","alias_value":"1501.03419v4","created_at":"2026-05-18T00:51:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1501.03419","created_at":"2026-05-18T00:51:03Z"},{"alias_kind":"pith_short_12","alias_value":"LSVSRZDY23KX","created_at":"2026-05-18T12:29:29Z"},{"alias_kind":"pith_short_16","alias_value":"LSVSRZDY23KXUCEJ","created_at":"2026-05-18T12:29:29Z"},{"alias_kind":"pith_short_8","alias_value":"LSVSRZDY","created_at":"2026-05-18T12:29:29Z"}],"graph_snapshots":[{"event_id":"sha256:1962a38dfb15368a1e5552dce7476add8e909771dd6768c8a80ad586e64924f5","target":"graph","created_at":"2026-05-18T00:51:03Z","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":"The joint spectral radius of a pair of 2x2 real matrices $(A_0,A_1)\\in M_2(\\mathbb{R})^2$ is defined to be $r(A_0,A_1)= \\limsup_{n\\to\\infty} \\max \\{\\|A_{i_1}...A_{i_n}\\|^{1/n}: i_j\\in\\{0,1\\}\\}$, the optimal growth rate of the norm of products of these matrices. The Lagarias-Wang finiteness conjecture, asserting that $r(A_0,A_1)$ is always the nth root of the spectral radius of some length-n product $A_{i_1}...A_{i_n}$, has been refuted by Bousch & Mairesse, with subsequent counterexamples presented by Blondel, Theys & Vladimirov; Kozyakin; Hare, Morris, Sidorov & Theys. In this article we intr","authors_text":"Mark Pollicott, Oliver Jenkinson","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-01-14T17:32:00Z","title":"Joint spectral radius, Sturmian measures, and the finiteness conjecture"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.03419","kind":"arxiv","version":4},"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":"sha256:36ae462d0b2be654d02d23af3e676ca14e673a12ece44b88fdd60bca0aa05590","target":"record","created_at":"2026-05-18T00:51:03Z","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":"796c153d00bfca27b5fbdcc1f159538bbc0d31b739c0ddf2c0b66b5f1dca8697","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-01-14T17:32:00Z","title_canon_sha256":"0ba843f4c4c68a40caa825341a439868d4a35da9dfdd37f53dc67aed5bd2e63a"},"schema_version":"1.0","source":{"id":"1501.03419","kind":"arxiv","version":4}},"canonical_sha256":"5cab28e478d6d57a088954adfdd8dc959da5f29e81edc013fb5cdcd37ba900a2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5cab28e478d6d57a088954adfdd8dc959da5f29e81edc013fb5cdcd37ba900a2","first_computed_at":"2026-05-18T00:51:03.458955Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:51:03.458955Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"thUx8j7t4dDKfbzgWuTXXXYR7cEKH21MHDPFfVR+yxVSqIQAcDMNPSEBsopYG98NsyD/AnHBM7gVGcFaO6iTBA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:51:03.459341Z","signed_message":"canonical_sha256_bytes"},"source_id":"1501.03419","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:36ae462d0b2be654d02d23af3e676ca14e673a12ece44b88fdd60bca0aa05590","sha256:1962a38dfb15368a1e5552dce7476add8e909771dd6768c8a80ad586e64924f5"],"state_sha256":"6ac5b5dcf030e0876e42c35e36c0dcfb32cdcebb426e0e8c22d2b646044bd767"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NXHuiaa+Py13a9bZSCligHqE9h2ETFo2GC4Rm4sHkURQ8bdDHMDSbTK6ZJU0z7b1CnBapvu4MDG4QlE0NU9VCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-11T14:07:25.458236Z","bundle_sha256":"659e2658a96386b46274f56fef8b28686c2e3b131e53ed4e86405629224a40bd"}}