{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:N6KK64ADFWPA5QJQBJEICIFWUF","short_pith_number":"pith:N6KK64AD","canonical_record":{"source":{"id":"2606.06859","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2026-06-05T03:03:17Z","cross_cats_sorted":["math.CO","math.DS"],"title_canon_sha256":"e7cdaef991bd72d3400b2849acf5ae5cfe1bf1e0cbd4a81315ae67cf32b49b43","abstract_canon_sha256":"a0729fdbdf32c11f4b86ce1097efe413e5abb7f4db643ad5b862c71b6fa2580d"},"schema_version":"1.0"},"canonical_sha256":"6f94af70032d9e0ec1300a488120b6a17ab3fd0826fe1b3081716fe059be7101","source":{"kind":"arxiv","id":"2606.06859","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.06859","created_at":"2026-06-08T01:04:32Z"},{"alias_kind":"arxiv_version","alias_value":"2606.06859v1","created_at":"2026-06-08T01:04:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.06859","created_at":"2026-06-08T01:04:32Z"},{"alias_kind":"pith_short_12","alias_value":"N6KK64ADFWPA","created_at":"2026-06-08T01:04:32Z"},{"alias_kind":"pith_short_16","alias_value":"N6KK64ADFWPA5QJQ","created_at":"2026-06-08T01:04:32Z"},{"alias_kind":"pith_short_8","alias_value":"N6KK64AD","created_at":"2026-06-08T01:04:32Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:N6KK64ADFWPA5QJQBJEICIFWUF","target":"record","payload":{"canonical_record":{"source":{"id":"2606.06859","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2026-06-05T03:03:17Z","cross_cats_sorted":["math.CO","math.DS"],"title_canon_sha256":"e7cdaef991bd72d3400b2849acf5ae5cfe1bf1e0cbd4a81315ae67cf32b49b43","abstract_canon_sha256":"a0729fdbdf32c11f4b86ce1097efe413e5abb7f4db643ad5b862c71b6fa2580d"},"schema_version":"1.0"},"canonical_sha256":"6f94af70032d9e0ec1300a488120b6a17ab3fd0826fe1b3081716fe059be7101","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-08T01:04:32.227826Z","signature_b64":"LnWjw+T8FBZGVmGK+20AIgAFNc4IoqvaXn7j2cBv6lq3+bv6Ps35miBvD2BRguG+qpdT6YvfXpCvDP1XqxI/Aw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6f94af70032d9e0ec1300a488120b6a17ab3fd0826fe1b3081716fe059be7101","last_reissued_at":"2026-06-08T01:04:32.227045Z","signature_status":"signed_v1","first_computed_at":"2026-06-08T01:04:32.227045Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2606.06859","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":"2026-06-08T01:04:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sXMxtYznIWUOocxB6Ti7vP+2ppd6yVoscFocKro/SYp2k9+qF+HXuCKsFdWynJP21/ktfEeShrqvv/B7ONyMBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-04T04:24:33.685725Z"},"content_sha256":"361d6729914b98e48f217376b868b05837e69256a5c93cde38c9513f01830206","schema_version":"1.0","event_id":"sha256:361d6729914b98e48f217376b868b05837e69256a5c93cde38c9513f01830206"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:N6KK64ADFWPA5QJQBJEICIFWUF","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Rectangular Finite Free Heat Flow","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO","math.DS"],"primary_cat":"math.PR","authors_text":"Cesar Cuenca, Colin McSwiggen","submitted_at":"2026-06-05T03:03:17Z","abstract_excerpt":"We define and study the rectangular finite free heat flow, a dynamical system on polynomials that plays the role of the heat equation in the setting of rectangular finite free probability. We show several equivalent characterizations of the evolution (including PDE and gradient flow formulations), establish basic properties of the dynamics, and determine the asymptotic distributions of the polynomial roots in the long-time and high-degree limits. We also discuss connections with Calogero-Moser systems and Dunkl processes, and we show that the rectangular finite free heat flow describes the mea"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.06859","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/2606.06859/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":"2026-06-08T01:04:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"u1DALfByGLA9fFgTB5ANKS4+TDiuGe23rgwdZ+owBuNMMKhU0xXNkB/7JK0LDTgQG1KU9x4Cc86eZVTWIu4TDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-04T04:24:33.686103Z"},"content_sha256":"ebf74efe6b054d8dbc68d739357a2ef9107d677ee5992d6389775aa727def639","schema_version":"1.0","event_id":"sha256:ebf74efe6b054d8dbc68d739357a2ef9107d677ee5992d6389775aa727def639"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/N6KK64ADFWPA5QJQBJEICIFWUF/bundle.json","state_url":"https://pith.science/pith/N6KK64ADFWPA5QJQBJEICIFWUF/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/N6KK64ADFWPA5QJQBJEICIFWUF/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":"2026-07-04T04:24:33Z","links":{"resolver":"https://pith.science/pith/N6KK64ADFWPA5QJQBJEICIFWUF","bundle":"https://pith.science/pith/N6KK64ADFWPA5QJQBJEICIFWUF/bundle.json","state":"https://pith.science/pith/N6KK64ADFWPA5QJQBJEICIFWUF/state.json","well_known_bundle":"https://pith.science/.well-known/pith/N6KK64ADFWPA5QJQBJEICIFWUF/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:N6KK64ADFWPA5QJQBJEICIFWUF","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":"a0729fdbdf32c11f4b86ce1097efe413e5abb7f4db643ad5b862c71b6fa2580d","cross_cats_sorted":["math.CO","math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2026-06-05T03:03:17Z","title_canon_sha256":"e7cdaef991bd72d3400b2849acf5ae5cfe1bf1e0cbd4a81315ae67cf32b49b43"},"schema_version":"1.0","source":{"id":"2606.06859","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.06859","created_at":"2026-06-08T01:04:32Z"},{"alias_kind":"arxiv_version","alias_value":"2606.06859v1","created_at":"2026-06-08T01:04:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.06859","created_at":"2026-06-08T01:04:32Z"},{"alias_kind":"pith_short_12","alias_value":"N6KK64ADFWPA","created_at":"2026-06-08T01:04:32Z"},{"alias_kind":"pith_short_16","alias_value":"N6KK64ADFWPA5QJQ","created_at":"2026-06-08T01:04:32Z"},{"alias_kind":"pith_short_8","alias_value":"N6KK64AD","created_at":"2026-06-08T01:04:32Z"}],"graph_snapshots":[{"event_id":"sha256:ebf74efe6b054d8dbc68d739357a2ef9107d677ee5992d6389775aa727def639","target":"graph","created_at":"2026-06-08T01:04:32Z","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/2606.06859/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We define and study the rectangular finite free heat flow, a dynamical system on polynomials that plays the role of the heat equation in the setting of rectangular finite free probability. We show several equivalent characterizations of the evolution (including PDE and gradient flow formulations), establish basic properties of the dynamics, and determine the asymptotic distributions of the polynomial roots in the long-time and high-degree limits. We also discuss connections with Calogero-Moser systems and Dunkl processes, and we show that the rectangular finite free heat flow describes the mea","authors_text":"Cesar Cuenca, Colin McSwiggen","cross_cats":["math.CO","math.DS"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2026-06-05T03:03:17Z","title":"The Rectangular Finite Free Heat Flow"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.06859","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":"sha256:361d6729914b98e48f217376b868b05837e69256a5c93cde38c9513f01830206","target":"record","created_at":"2026-06-08T01:04:32Z","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":"a0729fdbdf32c11f4b86ce1097efe413e5abb7f4db643ad5b862c71b6fa2580d","cross_cats_sorted":["math.CO","math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2026-06-05T03:03:17Z","title_canon_sha256":"e7cdaef991bd72d3400b2849acf5ae5cfe1bf1e0cbd4a81315ae67cf32b49b43"},"schema_version":"1.0","source":{"id":"2606.06859","kind":"arxiv","version":1}},"canonical_sha256":"6f94af70032d9e0ec1300a488120b6a17ab3fd0826fe1b3081716fe059be7101","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6f94af70032d9e0ec1300a488120b6a17ab3fd0826fe1b3081716fe059be7101","first_computed_at":"2026-06-08T01:04:32.227045Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-08T01:04:32.227045Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"LnWjw+T8FBZGVmGK+20AIgAFNc4IoqvaXn7j2cBv6lq3+bv6Ps35miBvD2BRguG+qpdT6YvfXpCvDP1XqxI/Aw==","signature_status":"signed_v1","signed_at":"2026-06-08T01:04:32.227826Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.06859","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:361d6729914b98e48f217376b868b05837e69256a5c93cde38c9513f01830206","sha256:ebf74efe6b054d8dbc68d739357a2ef9107d677ee5992d6389775aa727def639"],"state_sha256":"ba4f4eab87b7c26c4be2b28af0a3275855f794ec015dec4729134ff29895d8de"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YUP24Ybl1f7kA9RGZhBdwth5HHxuIxEePz2r2TESU+y+Jh/Ml1fZeKvZUp9XUIrPL+vzHwuHlPaxjwbTjS2ADQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-04T04:24:33.688050Z","bundle_sha256":"bd4901a83020ea8154537a20ed5a06ae8c10b2bab18dc81965f2d988ab4bac85"}}