{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:4WWX7FCIPSOANOVXPGMOPNTGRQ","short_pith_number":"pith:4WWX7FCI","canonical_record":{"source":{"id":"1108.3587","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"nlin.SI","submitted_at":"2011-08-17T22:03:13Z","cross_cats_sorted":["math.RT"],"title_canon_sha256":"44080a5268f9d3206228948f172eef615af631a54f580f0ed8fc840bb1b5625d","abstract_canon_sha256":"31e46442bd47fd04b95e476055522e9fbb06bd410a278a01adf892e021e2f509"},"schema_version":"1.0"},"canonical_sha256":"e5ad7f94487c9c06bab77998e7b6668c03e9cf86ef7e490d8e3046e4e26575b6","source":{"kind":"arxiv","id":"1108.3587","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1108.3587","created_at":"2026-05-18T03:04:59Z"},{"alias_kind":"arxiv_version","alias_value":"1108.3587v3","created_at":"2026-05-18T03:04:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1108.3587","created_at":"2026-05-18T03:04:59Z"},{"alias_kind":"pith_short_12","alias_value":"4WWX7FCIPSOA","created_at":"2026-05-18T12:26:20Z"},{"alias_kind":"pith_short_16","alias_value":"4WWX7FCIPSOANOVX","created_at":"2026-05-18T12:26:20Z"},{"alias_kind":"pith_short_8","alias_value":"4WWX7FCI","created_at":"2026-05-18T12:26:20Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:4WWX7FCIPSOANOVXPGMOPNTGRQ","target":"record","payload":{"canonical_record":{"source":{"id":"1108.3587","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"nlin.SI","submitted_at":"2011-08-17T22:03:13Z","cross_cats_sorted":["math.RT"],"title_canon_sha256":"44080a5268f9d3206228948f172eef615af631a54f580f0ed8fc840bb1b5625d","abstract_canon_sha256":"31e46442bd47fd04b95e476055522e9fbb06bd410a278a01adf892e021e2f509"},"schema_version":"1.0"},"canonical_sha256":"e5ad7f94487c9c06bab77998e7b6668c03e9cf86ef7e490d8e3046e4e26575b6","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:04:59.806659Z","signature_b64":"GO8Y+kb7w+VXp6QMXJFrl7xm3CBnvCX4RvDuCHpc4nvU+dl3EGpOdvcRMDjN8/jm/KuSm3r4jJ34VvLVyKeZBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e5ad7f94487c9c06bab77998e7b6668c03e9cf86ef7e490d8e3046e4e26575b6","last_reissued_at":"2026-05-18T03:04:59.806091Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:04:59.806091Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1108.3587","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":"2026-05-18T03:04:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9wW2FbltASRo11FY4/nzJkuv3lRds++E7VxqUiORUPLdKIk823U32zj35DrmtOpGaeYm7vOz6CMiPliD1wMjAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T05:51:45.880790Z"},"content_sha256":"8782ddc2f858dea60f7aa34a47163654e4e1e84829e49465c46a55a2acf96ae4","schema_version":"1.0","event_id":"sha256:8782ddc2f858dea60f7aa34a47163654e4e1e84829e49465c46a55a2acf96ae4"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:4WWX7FCIPSOANOVXPGMOPNTGRQ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A Centerless Virasoro Algebra of Master Symmetries for the Ablowitz-Ladik Hierarchy","license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"nlin.SI","authors_text":"Didier Vanderstichelen, Luc Haine","submitted_at":"2011-08-17T22:03:13Z","abstract_excerpt":"We show that the (semi-infinite) Ablowitz-Ladik (AL) hierarchy admits a centerless Virasoro algebra of master symmetries in the sense of Fuchssteiner [Progr. Theoret. Phys. 70 (1983), 1508-1522]. An explicit expression for these symmetries is given in terms of a slight generalization of the Cantero, Moral and Vel\\'azquez (CMV) matrices [Linear Algebra Appl. 362 (2003), 29-56] and their action on the tau-functions of the hierarchy is described. The use of the CMV matrices turns out to be crucial for obtaining a Lax pair representation of the master symmetries. The AL hierarchy seems to be the f"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1108.3587","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":"2026-05-18T03:04:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MRc+LusuX9nJGnr+NA2Y+swnS6MthPxwqj7nFYr5t65KASXumpuOy7BEZTr0C4RdOEUP5sl/kVdx8GzSdnlmBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T05:51:45.881138Z"},"content_sha256":"060fa6658daf41fac090930b5acc0f2f696a86e001d54aab0abf66d23dcdf1f5","schema_version":"1.0","event_id":"sha256:060fa6658daf41fac090930b5acc0f2f696a86e001d54aab0abf66d23dcdf1f5"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/4WWX7FCIPSOANOVXPGMOPNTGRQ/bundle.json","state_url":"https://pith.science/pith/4WWX7FCIPSOANOVXPGMOPNTGRQ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/4WWX7FCIPSOANOVXPGMOPNTGRQ/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":"2026-06-23T05:51:45Z","links":{"resolver":"https://pith.science/pith/4WWX7FCIPSOANOVXPGMOPNTGRQ","bundle":"https://pith.science/pith/4WWX7FCIPSOANOVXPGMOPNTGRQ/bundle.json","state":"https://pith.science/pith/4WWX7FCIPSOANOVXPGMOPNTGRQ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/4WWX7FCIPSOANOVXPGMOPNTGRQ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:4WWX7FCIPSOANOVXPGMOPNTGRQ","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":"31e46442bd47fd04b95e476055522e9fbb06bd410a278a01adf892e021e2f509","cross_cats_sorted":["math.RT"],"license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"nlin.SI","submitted_at":"2011-08-17T22:03:13Z","title_canon_sha256":"44080a5268f9d3206228948f172eef615af631a54f580f0ed8fc840bb1b5625d"},"schema_version":"1.0","source":{"id":"1108.3587","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1108.3587","created_at":"2026-05-18T03:04:59Z"},{"alias_kind":"arxiv_version","alias_value":"1108.3587v3","created_at":"2026-05-18T03:04:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1108.3587","created_at":"2026-05-18T03:04:59Z"},{"alias_kind":"pith_short_12","alias_value":"4WWX7FCIPSOA","created_at":"2026-05-18T12:26:20Z"},{"alias_kind":"pith_short_16","alias_value":"4WWX7FCIPSOANOVX","created_at":"2026-05-18T12:26:20Z"},{"alias_kind":"pith_short_8","alias_value":"4WWX7FCI","created_at":"2026-05-18T12:26:20Z"}],"graph_snapshots":[{"event_id":"sha256:060fa6658daf41fac090930b5acc0f2f696a86e001d54aab0abf66d23dcdf1f5","target":"graph","created_at":"2026-05-18T03:04:59Z","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":"We show that the (semi-infinite) Ablowitz-Ladik (AL) hierarchy admits a centerless Virasoro algebra of master symmetries in the sense of Fuchssteiner [Progr. Theoret. Phys. 70 (1983), 1508-1522]. An explicit expression for these symmetries is given in terms of a slight generalization of the Cantero, Moral and Vel\\'azquez (CMV) matrices [Linear Algebra Appl. 362 (2003), 29-56] and their action on the tau-functions of the hierarchy is described. The use of the CMV matrices turns out to be crucial for obtaining a Lax pair representation of the master symmetries. The AL hierarchy seems to be the f","authors_text":"Didier Vanderstichelen, Luc Haine","cross_cats":["math.RT"],"headline":"","license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"nlin.SI","submitted_at":"2011-08-17T22:03:13Z","title":"A Centerless Virasoro Algebra of Master Symmetries for the Ablowitz-Ladik Hierarchy"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1108.3587","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":"sha256:8782ddc2f858dea60f7aa34a47163654e4e1e84829e49465c46a55a2acf96ae4","target":"record","created_at":"2026-05-18T03:04:59Z","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":"31e46442bd47fd04b95e476055522e9fbb06bd410a278a01adf892e021e2f509","cross_cats_sorted":["math.RT"],"license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"nlin.SI","submitted_at":"2011-08-17T22:03:13Z","title_canon_sha256":"44080a5268f9d3206228948f172eef615af631a54f580f0ed8fc840bb1b5625d"},"schema_version":"1.0","source":{"id":"1108.3587","kind":"arxiv","version":3}},"canonical_sha256":"e5ad7f94487c9c06bab77998e7b6668c03e9cf86ef7e490d8e3046e4e26575b6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e5ad7f94487c9c06bab77998e7b6668c03e9cf86ef7e490d8e3046e4e26575b6","first_computed_at":"2026-05-18T03:04:59.806091Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:04:59.806091Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"GO8Y+kb7w+VXp6QMXJFrl7xm3CBnvCX4RvDuCHpc4nvU+dl3EGpOdvcRMDjN8/jm/KuSm3r4jJ34VvLVyKeZBw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:04:59.806659Z","signed_message":"canonical_sha256_bytes"},"source_id":"1108.3587","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8782ddc2f858dea60f7aa34a47163654e4e1e84829e49465c46a55a2acf96ae4","sha256:060fa6658daf41fac090930b5acc0f2f696a86e001d54aab0abf66d23dcdf1f5"],"state_sha256":"ad052e3502d6e4002d1badf527a6784e27675bd2eeac4464faf5f8a19b4f1f33"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tuQrVdF36gfcaFEm7i6EAxZhOQe3kO8rJ0NK6XeaUo2Nsq1IOxNz3D8eiaHZ53IosP8VNqj46ueFidCNuO3AAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T05:51:45.883125Z","bundle_sha256":"534fd16f4b0c19c69f8acd3b0b604edc2dbb302b9051f3f56add904f5a079ad4"}}