{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:UAUNR5LNSOK5LQP4JNJD5T5S7V","short_pith_number":"pith:UAUNR5LN","canonical_record":{"source":{"id":"1212.2774","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2012-12-12T11:30:34Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"1aeb3478837ac9a4bd1175607d431de65c110f1bfd204d800da174a80a0ed05f","abstract_canon_sha256":"4d4a68cb1f5c7c4bd8fbea436c303843ab222c82d51c627d030c478a640a73b0"},"schema_version":"1.0"},"canonical_sha256":"a028d8f56d9395d5c1fc4b523ecfb2fd5c482b04462b682ecc0c486cc43504a5","source":{"kind":"arxiv","id":"1212.2774","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1212.2774","created_at":"2026-05-18T02:26:01Z"},{"alias_kind":"arxiv_version","alias_value":"1212.2774v1","created_at":"2026-05-18T02:26:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1212.2774","created_at":"2026-05-18T02:26:01Z"},{"alias_kind":"pith_short_12","alias_value":"UAUNR5LNSOK5","created_at":"2026-05-18T12:27:23Z"},{"alias_kind":"pith_short_16","alias_value":"UAUNR5LNSOK5LQP4","created_at":"2026-05-18T12:27:23Z"},{"alias_kind":"pith_short_8","alias_value":"UAUNR5LN","created_at":"2026-05-18T12:27:23Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:UAUNR5LNSOK5LQP4JNJD5T5S7V","target":"record","payload":{"canonical_record":{"source":{"id":"1212.2774","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2012-12-12T11:30:34Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"1aeb3478837ac9a4bd1175607d431de65c110f1bfd204d800da174a80a0ed05f","abstract_canon_sha256":"4d4a68cb1f5c7c4bd8fbea436c303843ab222c82d51c627d030c478a640a73b0"},"schema_version":"1.0"},"canonical_sha256":"a028d8f56d9395d5c1fc4b523ecfb2fd5c482b04462b682ecc0c486cc43504a5","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:26:01.231219Z","signature_b64":"ZZqMwY7GJyKxfsQ2DE4vHkfK9pRkn27CrMeWifcxthNPc8SAhirDvPHfjc4uIBaJ9Hk0MiQ4jvA3vuSpemzQDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a028d8f56d9395d5c1fc4b523ecfb2fd5c482b04462b682ecc0c486cc43504a5","last_reissued_at":"2026-05-18T02:26:01.230622Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:26:01.230622Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1212.2774","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":"2026-05-18T02:26:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pfAu2GcGu9FJHWIT0P+o1coy/xKy32o00TMep3ljLTNc30iqqDFLCOjQQ3s4i4DtmqFASrHkQGrjcIIBts5WAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T12:45:16.770476Z"},"content_sha256":"c73906de0d10ed22806ad3d6bb068ecfe83468f44d052fdb0c96965741ab8571","schema_version":"1.0","event_id":"sha256:c73906de0d10ed22806ad3d6bb068ecfe83468f44d052fdb0c96965741ab8571"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:UAUNR5LNSOK5LQP4JNJD5T5S7V","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Ultradiscrete Soliton Systems and Combinatorial Representation Theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.QA","authors_text":"Reiho Sakamoto","submitted_at":"2012-12-12T11:30:34Z","abstract_excerpt":"This lecture note is intended to be a brief introduction to a recent development on the interplay between the ultradiscrete (or tropical) soliton systems and the combinatorial representation theory. We will concentrate on the simplest cases which admit elementary explanations without losing essential ideas of the theory. In particular we give definitions for the main constructions corresponding to the vector representation of type $A^{(1)}_1$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.2774","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":""},"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":"2026-05-18T02:26:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vnl7XXJlruH8wWqeJm8BFg/uTdK2bdlK6Syxwql6f0gKa9kW1b4EN63beFFG8hhj2yTBMRisc1Ge2ttAuLdLAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T12:45:16.771082Z"},"content_sha256":"aab7da29032226c66399a3d5af7d85c8ca9bcce2f35888a952cbc9ea718ee92a","schema_version":"1.0","event_id":"sha256:aab7da29032226c66399a3d5af7d85c8ca9bcce2f35888a952cbc9ea718ee92a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/UAUNR5LNSOK5LQP4JNJD5T5S7V/bundle.json","state_url":"https://pith.science/pith/UAUNR5LNSOK5LQP4JNJD5T5S7V/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/UAUNR5LNSOK5LQP4JNJD5T5S7V/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":"2026-05-30T12:45:16Z","links":{"resolver":"https://pith.science/pith/UAUNR5LNSOK5LQP4JNJD5T5S7V","bundle":"https://pith.science/pith/UAUNR5LNSOK5LQP4JNJD5T5S7V/bundle.json","state":"https://pith.science/pith/UAUNR5LNSOK5LQP4JNJD5T5S7V/state.json","well_known_bundle":"https://pith.science/.well-known/pith/UAUNR5LNSOK5LQP4JNJD5T5S7V/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:UAUNR5LNSOK5LQP4JNJD5T5S7V","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":"4d4a68cb1f5c7c4bd8fbea436c303843ab222c82d51c627d030c478a640a73b0","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2012-12-12T11:30:34Z","title_canon_sha256":"1aeb3478837ac9a4bd1175607d431de65c110f1bfd204d800da174a80a0ed05f"},"schema_version":"1.0","source":{"id":"1212.2774","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1212.2774","created_at":"2026-05-18T02:26:01Z"},{"alias_kind":"arxiv_version","alias_value":"1212.2774v1","created_at":"2026-05-18T02:26:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1212.2774","created_at":"2026-05-18T02:26:01Z"},{"alias_kind":"pith_short_12","alias_value":"UAUNR5LNSOK5","created_at":"2026-05-18T12:27:23Z"},{"alias_kind":"pith_short_16","alias_value":"UAUNR5LNSOK5LQP4","created_at":"2026-05-18T12:27:23Z"},{"alias_kind":"pith_short_8","alias_value":"UAUNR5LN","created_at":"2026-05-18T12:27:23Z"}],"graph_snapshots":[{"event_id":"sha256:aab7da29032226c66399a3d5af7d85c8ca9bcce2f35888a952cbc9ea718ee92a","target":"graph","created_at":"2026-05-18T02:26:01Z","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":"This lecture note is intended to be a brief introduction to a recent development on the interplay between the ultradiscrete (or tropical) soliton systems and the combinatorial representation theory. We will concentrate on the simplest cases which admit elementary explanations without losing essential ideas of the theory. In particular we give definitions for the main constructions corresponding to the vector representation of type $A^{(1)}_1$.","authors_text":"Reiho Sakamoto","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2012-12-12T11:30:34Z","title":"Ultradiscrete Soliton Systems and Combinatorial Representation Theory"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.2774","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:c73906de0d10ed22806ad3d6bb068ecfe83468f44d052fdb0c96965741ab8571","target":"record","created_at":"2026-05-18T02:26:01Z","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":"4d4a68cb1f5c7c4bd8fbea436c303843ab222c82d51c627d030c478a640a73b0","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2012-12-12T11:30:34Z","title_canon_sha256":"1aeb3478837ac9a4bd1175607d431de65c110f1bfd204d800da174a80a0ed05f"},"schema_version":"1.0","source":{"id":"1212.2774","kind":"arxiv","version":1}},"canonical_sha256":"a028d8f56d9395d5c1fc4b523ecfb2fd5c482b04462b682ecc0c486cc43504a5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a028d8f56d9395d5c1fc4b523ecfb2fd5c482b04462b682ecc0c486cc43504a5","first_computed_at":"2026-05-18T02:26:01.230622Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:26:01.230622Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ZZqMwY7GJyKxfsQ2DE4vHkfK9pRkn27CrMeWifcxthNPc8SAhirDvPHfjc4uIBaJ9Hk0MiQ4jvA3vuSpemzQDw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:26:01.231219Z","signed_message":"canonical_sha256_bytes"},"source_id":"1212.2774","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c73906de0d10ed22806ad3d6bb068ecfe83468f44d052fdb0c96965741ab8571","sha256:aab7da29032226c66399a3d5af7d85c8ca9bcce2f35888a952cbc9ea718ee92a"],"state_sha256":"9d312fdc54700a0f4f6ac304213ed814091246aff842127f67f56f7b2acb792f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Rq4nMCRUyx0iPnnLX12gFqwT5s5KTP8BsysfHIgv6g76e1i7hcLCuKRa6jfufzN+3BKykQRvJ5roVDFMH7CUCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T12:45:16.773601Z","bundle_sha256":"05358d3679334e846f19c7468d20ddcebea1a5f508ca2a954d22e8fc78d7ab2c"}}