{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:PBUHLWELKBH6CMSBPRONZCXHLX","short_pith_number":"pith:PBUHLWEL","canonical_record":{"source":{"id":"1010.0927","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2010-10-05T15:58:05Z","cross_cats_sorted":["hep-th","math.GT"],"title_canon_sha256":"29f531ee881118cc1f5ad5a93bd769d40a2af1cb15e71530e39fc89b1c8370a2","abstract_canon_sha256":"2c09efbe775bbfb7d8baf1a4c15e6c721b807bb7fab114217103a9ef326eefc6"},"schema_version":"1.0"},"canonical_sha256":"786875d88b504fe132417c5cdc8ae75de69d6148f257439ef1d569559d5f0d1f","source":{"kind":"arxiv","id":"1010.0927","version":5},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1010.0927","created_at":"2026-05-18T03:53:42Z"},{"alias_kind":"arxiv_version","alias_value":"1010.0927v5","created_at":"2026-05-18T03:53:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1010.0927","created_at":"2026-05-18T03:53:42Z"},{"alias_kind":"pith_short_12","alias_value":"PBUHLWELKBH6","created_at":"2026-05-18T12:26:12Z"},{"alias_kind":"pith_short_16","alias_value":"PBUHLWELKBH6CMSB","created_at":"2026-05-18T12:26:12Z"},{"alias_kind":"pith_short_8","alias_value":"PBUHLWEL","created_at":"2026-05-18T12:26:12Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:PBUHLWELKBH6CMSBPRONZCXHLX","target":"record","payload":{"canonical_record":{"source":{"id":"1010.0927","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2010-10-05T15:58:05Z","cross_cats_sorted":["hep-th","math.GT"],"title_canon_sha256":"29f531ee881118cc1f5ad5a93bd769d40a2af1cb15e71530e39fc89b1c8370a2","abstract_canon_sha256":"2c09efbe775bbfb7d8baf1a4c15e6c721b807bb7fab114217103a9ef326eefc6"},"schema_version":"1.0"},"canonical_sha256":"786875d88b504fe132417c5cdc8ae75de69d6148f257439ef1d569559d5f0d1f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:53:42.627300Z","signature_b64":"mI/VIa3JHO0z1A3WOKU5Y2IMhrAHnp3UPH59c7O2nToy4Uc4DvDsgROupsym/xHbLC44yEjuFNB6HhOcLbcIBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"786875d88b504fe132417c5cdc8ae75de69d6148f257439ef1d569559d5f0d1f","last_reissued_at":"2026-05-18T03:53:42.626777Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:53:42.626777Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1010.0927","source_version":5,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:53:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Lu38QNDyseb3c+diJY8f4zHIFANxVs1N0TDOMTYOrn1zOML+C75WGkcYgeiOt4e4YKLPj1tbzuM+1kFbEf49DA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T06:37:16.463105Z"},"content_sha256":"b89ceb9b677958f96975186dc231d72380b2b38346c6514562578469eb5f85f3","schema_version":"1.0","event_id":"sha256:b89ceb9b677958f96975186dc231d72380b2b38346c6514562578469eb5f85f3"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:PBUHLWELKBH6CMSBPRONZCXHLX","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Analyticity of the planar limit of a matrix model","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th","math.GT"],"primary_cat":"math.CA","authors_text":"Ionel Popescu, Stavros Garoufalidis","submitted_at":"2010-10-05T15:58:05Z","abstract_excerpt":"Using Chebyshev polynomials combined with some mild combinatorics, we provide a new formula for the analytical planar limit of a random matrix model with a one-cut potential $V$. For potentials $V(x)=x^{2}/2-\\sum_{n\\ge1}a_{n}x^{n}/n$, as a power series in all $a_{n}$, the formal Taylor expansion of the analytic planar limit is exactly the formal planar limit. In the case $V$ is analytic in infinitely many variables $\\{a_{n}\\}_{n\\ge1}$ (on the appropriate spaces), the planar limit is also an analytic function in infinitely many variables and we give quantitative versions of where this is define"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1010.0927","kind":"arxiv","version":5},"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":"2026-05-18T03:53:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NyjIjurZ1VDo1PsUL1QRYRU1hWmG4SUdehukUiRwjyuOStoNrUEzFRvi/vB90SA3gVQ0fWz59+s9//7bIUfnAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T06:37:16.463480Z"},"content_sha256":"7df822cecad03089830c9fedea0ec596eecaf2b13b08e9d067d7673cb3bb5e29","schema_version":"1.0","event_id":"sha256:7df822cecad03089830c9fedea0ec596eecaf2b13b08e9d067d7673cb3bb5e29"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/PBUHLWELKBH6CMSBPRONZCXHLX/bundle.json","state_url":"https://pith.science/pith/PBUHLWELKBH6CMSBPRONZCXHLX/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/PBUHLWELKBH6CMSBPRONZCXHLX/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":"2026-06-24T06:37:16Z","links":{"resolver":"https://pith.science/pith/PBUHLWELKBH6CMSBPRONZCXHLX","bundle":"https://pith.science/pith/PBUHLWELKBH6CMSBPRONZCXHLX/bundle.json","state":"https://pith.science/pith/PBUHLWELKBH6CMSBPRONZCXHLX/state.json","well_known_bundle":"https://pith.science/.well-known/pith/PBUHLWELKBH6CMSBPRONZCXHLX/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:PBUHLWELKBH6CMSBPRONZCXHLX","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":"2c09efbe775bbfb7d8baf1a4c15e6c721b807bb7fab114217103a9ef326eefc6","cross_cats_sorted":["hep-th","math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2010-10-05T15:58:05Z","title_canon_sha256":"29f531ee881118cc1f5ad5a93bd769d40a2af1cb15e71530e39fc89b1c8370a2"},"schema_version":"1.0","source":{"id":"1010.0927","kind":"arxiv","version":5}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1010.0927","created_at":"2026-05-18T03:53:42Z"},{"alias_kind":"arxiv_version","alias_value":"1010.0927v5","created_at":"2026-05-18T03:53:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1010.0927","created_at":"2026-05-18T03:53:42Z"},{"alias_kind":"pith_short_12","alias_value":"PBUHLWELKBH6","created_at":"2026-05-18T12:26:12Z"},{"alias_kind":"pith_short_16","alias_value":"PBUHLWELKBH6CMSB","created_at":"2026-05-18T12:26:12Z"},{"alias_kind":"pith_short_8","alias_value":"PBUHLWEL","created_at":"2026-05-18T12:26:12Z"}],"graph_snapshots":[{"event_id":"sha256:7df822cecad03089830c9fedea0ec596eecaf2b13b08e9d067d7673cb3bb5e29","target":"graph","created_at":"2026-05-18T03:53:42Z","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":"Using Chebyshev polynomials combined with some mild combinatorics, we provide a new formula for the analytical planar limit of a random matrix model with a one-cut potential $V$. For potentials $V(x)=x^{2}/2-\\sum_{n\\ge1}a_{n}x^{n}/n$, as a power series in all $a_{n}$, the formal Taylor expansion of the analytic planar limit is exactly the formal planar limit. In the case $V$ is analytic in infinitely many variables $\\{a_{n}\\}_{n\\ge1}$ (on the appropriate spaces), the planar limit is also an analytic function in infinitely many variables and we give quantitative versions of where this is define","authors_text":"Ionel Popescu, Stavros Garoufalidis","cross_cats":["hep-th","math.GT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2010-10-05T15:58:05Z","title":"Analyticity of the planar limit of a matrix model"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1010.0927","kind":"arxiv","version":5},"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:b89ceb9b677958f96975186dc231d72380b2b38346c6514562578469eb5f85f3","target":"record","created_at":"2026-05-18T03:53:42Z","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":"2c09efbe775bbfb7d8baf1a4c15e6c721b807bb7fab114217103a9ef326eefc6","cross_cats_sorted":["hep-th","math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2010-10-05T15:58:05Z","title_canon_sha256":"29f531ee881118cc1f5ad5a93bd769d40a2af1cb15e71530e39fc89b1c8370a2"},"schema_version":"1.0","source":{"id":"1010.0927","kind":"arxiv","version":5}},"canonical_sha256":"786875d88b504fe132417c5cdc8ae75de69d6148f257439ef1d569559d5f0d1f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"786875d88b504fe132417c5cdc8ae75de69d6148f257439ef1d569559d5f0d1f","first_computed_at":"2026-05-18T03:53:42.626777Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:53:42.626777Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"mI/VIa3JHO0z1A3WOKU5Y2IMhrAHnp3UPH59c7O2nToy4Uc4DvDsgROupsym/xHbLC44yEjuFNB6HhOcLbcIBA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:53:42.627300Z","signed_message":"canonical_sha256_bytes"},"source_id":"1010.0927","source_kind":"arxiv","source_version":5}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b89ceb9b677958f96975186dc231d72380b2b38346c6514562578469eb5f85f3","sha256:7df822cecad03089830c9fedea0ec596eecaf2b13b08e9d067d7673cb3bb5e29"],"state_sha256":"6cb53ed9b4867ee6ef9dd2daa331d6f35490fe06fb72df13b8afb87ebb23f2b2"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HlxCmiKu2Clps7xs2uubUHnZaq98jUI2IQtcgc1EL70nIwfd10W9dA1DiK1q0ycX9iusYLi9LCsY2N9pE6I4CA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-24T06:37:16.465426Z","bundle_sha256":"4bd6f9cae60ba99dc4b15108d9587ad1a7349941232c0e5127f5c16f9940b463"}}