{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:LWZ4ZLAGVVCWZQ62NRTUXH2EKS","short_pith_number":"pith:LWZ4ZLAG","canonical_record":{"source":{"id":"1110.3507","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-10-16T17:53:46Z","cross_cats_sorted":["math-ph","math.MP","nlin.SI"],"title_canon_sha256":"5504d4f8e6299718e175164b1051f25c43a15db0a6e1d93fe42af0e646291c8d","abstract_canon_sha256":"565d8793ae49ca141c28268465ae8ccc294b175d41eadf2d7162238533bcb1c1"},"schema_version":"1.0"},"canonical_sha256":"5db3ccac06ad456cc3da6c674b9f4454bf869e148c2d872a71832698171b7a31","source":{"kind":"arxiv","id":"1110.3507","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1110.3507","created_at":"2026-05-18T04:09:24Z"},{"alias_kind":"arxiv_version","alias_value":"1110.3507v2","created_at":"2026-05-18T04:09:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1110.3507","created_at":"2026-05-18T04:09:24Z"},{"alias_kind":"pith_short_12","alias_value":"LWZ4ZLAGVVCW","created_at":"2026-05-18T12:26:34Z"},{"alias_kind":"pith_short_16","alias_value":"LWZ4ZLAGVVCWZQ62","created_at":"2026-05-18T12:26:34Z"},{"alias_kind":"pith_short_8","alias_value":"LWZ4ZLAG","created_at":"2026-05-18T12:26:34Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:LWZ4ZLAGVVCWZQ62NRTUXH2EKS","target":"record","payload":{"canonical_record":{"source":{"id":"1110.3507","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-10-16T17:53:46Z","cross_cats_sorted":["math-ph","math.MP","nlin.SI"],"title_canon_sha256":"5504d4f8e6299718e175164b1051f25c43a15db0a6e1d93fe42af0e646291c8d","abstract_canon_sha256":"565d8793ae49ca141c28268465ae8ccc294b175d41eadf2d7162238533bcb1c1"},"schema_version":"1.0"},"canonical_sha256":"5db3ccac06ad456cc3da6c674b9f4454bf869e148c2d872a71832698171b7a31","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:09:24.989854Z","signature_b64":"WECqzjrOTbHvrlIrXqDaqeJkBoksw33Ly2h9OE39LrnbVVwWqTGwkYnraTlqWuimVCMXLsBZ2uwxIlHleqo6CQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5db3ccac06ad456cc3da6c674b9f4454bf869e148c2d872a71832698171b7a31","last_reissued_at":"2026-05-18T04:09:24.989207Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:09:24.989207Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1110.3507","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:09:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tYhHD1r91zbASDz1FLUYKSWqh7yajDjziCS/CsgJbiNLcnxK0HHbyAbvWlUIvUNwP6M6xkmCARFcLWi1RKMDDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T21:27:22.809888Z"},"content_sha256":"67000bdcbf353e2b929cf529cdeb217a66e51d39abe9b01e03dac099bf715cbc","schema_version":"1.0","event_id":"sha256:67000bdcbf353e2b929cf529cdeb217a66e51d39abe9b01e03dac099bf715cbc"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:LWZ4ZLAGVVCWZQ62NRTUXH2EKS","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"KP solitons, higher Bruhat and Tamari orders","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP","nlin.SI"],"primary_cat":"math.CO","authors_text":"Aristophanes Dimakis, Folkert Mueller-Hoissen","submitted_at":"2011-10-16T17:53:46Z","abstract_excerpt":"In a tropical approximation, any tree-shaped line soliton solution, a member of the simplest class of soliton solutions of the Kadomtsev-Petviashvili (KP-II) equation, determines a chain of planar rooted binary trees, connected by right rotation. More precisely, it determines a maximal chain of a Tamari lattice. We show that an analysis of these solutions naturally involves higher Bruhat and higher Tamari orders."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.3507","kind":"arxiv","version":2},"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":"2026-05-18T04:09:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IkXmViFSOJXfwAUvr5aFKzjP4n0CqgXXL9/VhbzwRqAMfxLNllV7KwukuNpb6Clzz4qZTOOFf4ufWlu26GYuBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T21:27:22.810548Z"},"content_sha256":"712a77950fd3208c8d7826ec0cfab407a570ec91d6f27fe93955eb5d8c9e4937","schema_version":"1.0","event_id":"sha256:712a77950fd3208c8d7826ec0cfab407a570ec91d6f27fe93955eb5d8c9e4937"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/LWZ4ZLAGVVCWZQ62NRTUXH2EKS/bundle.json","state_url":"https://pith.science/pith/LWZ4ZLAGVVCWZQ62NRTUXH2EKS/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/LWZ4ZLAGVVCWZQ62NRTUXH2EKS/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":"2026-06-11T21:27:22Z","links":{"resolver":"https://pith.science/pith/LWZ4ZLAGVVCWZQ62NRTUXH2EKS","bundle":"https://pith.science/pith/LWZ4ZLAGVVCWZQ62NRTUXH2EKS/bundle.json","state":"https://pith.science/pith/LWZ4ZLAGVVCWZQ62NRTUXH2EKS/state.json","well_known_bundle":"https://pith.science/.well-known/pith/LWZ4ZLAGVVCWZQ62NRTUXH2EKS/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:LWZ4ZLAGVVCWZQ62NRTUXH2EKS","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":"565d8793ae49ca141c28268465ae8ccc294b175d41eadf2d7162238533bcb1c1","cross_cats_sorted":["math-ph","math.MP","nlin.SI"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-10-16T17:53:46Z","title_canon_sha256":"5504d4f8e6299718e175164b1051f25c43a15db0a6e1d93fe42af0e646291c8d"},"schema_version":"1.0","source":{"id":"1110.3507","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1110.3507","created_at":"2026-05-18T04:09:24Z"},{"alias_kind":"arxiv_version","alias_value":"1110.3507v2","created_at":"2026-05-18T04:09:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1110.3507","created_at":"2026-05-18T04:09:24Z"},{"alias_kind":"pith_short_12","alias_value":"LWZ4ZLAGVVCW","created_at":"2026-05-18T12:26:34Z"},{"alias_kind":"pith_short_16","alias_value":"LWZ4ZLAGVVCWZQ62","created_at":"2026-05-18T12:26:34Z"},{"alias_kind":"pith_short_8","alias_value":"LWZ4ZLAG","created_at":"2026-05-18T12:26:34Z"}],"graph_snapshots":[{"event_id":"sha256:712a77950fd3208c8d7826ec0cfab407a570ec91d6f27fe93955eb5d8c9e4937","target":"graph","created_at":"2026-05-18T04:09:24Z","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":"In a tropical approximation, any tree-shaped line soliton solution, a member of the simplest class of soliton solutions of the Kadomtsev-Petviashvili (KP-II) equation, determines a chain of planar rooted binary trees, connected by right rotation. More precisely, it determines a maximal chain of a Tamari lattice. We show that an analysis of these solutions naturally involves higher Bruhat and higher Tamari orders.","authors_text":"Aristophanes Dimakis, Folkert Mueller-Hoissen","cross_cats":["math-ph","math.MP","nlin.SI"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-10-16T17:53:46Z","title":"KP solitons, higher Bruhat and Tamari orders"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.3507","kind":"arxiv","version":2},"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":"sha256:67000bdcbf353e2b929cf529cdeb217a66e51d39abe9b01e03dac099bf715cbc","target":"record","created_at":"2026-05-18T04:09:24Z","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":"565d8793ae49ca141c28268465ae8ccc294b175d41eadf2d7162238533bcb1c1","cross_cats_sorted":["math-ph","math.MP","nlin.SI"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-10-16T17:53:46Z","title_canon_sha256":"5504d4f8e6299718e175164b1051f25c43a15db0a6e1d93fe42af0e646291c8d"},"schema_version":"1.0","source":{"id":"1110.3507","kind":"arxiv","version":2}},"canonical_sha256":"5db3ccac06ad456cc3da6c674b9f4454bf869e148c2d872a71832698171b7a31","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5db3ccac06ad456cc3da6c674b9f4454bf869e148c2d872a71832698171b7a31","first_computed_at":"2026-05-18T04:09:24.989207Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:09:24.989207Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"WECqzjrOTbHvrlIrXqDaqeJkBoksw33Ly2h9OE39LrnbVVwWqTGwkYnraTlqWuimVCMXLsBZ2uwxIlHleqo6CQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:09:24.989854Z","signed_message":"canonical_sha256_bytes"},"source_id":"1110.3507","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:67000bdcbf353e2b929cf529cdeb217a66e51d39abe9b01e03dac099bf715cbc","sha256:712a77950fd3208c8d7826ec0cfab407a570ec91d6f27fe93955eb5d8c9e4937"],"state_sha256":"6086e3c90227690e48472c4046b16753386fdcd4b124c76dbfd9ef3606e8d135"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"n5tqemy0kZmyqjRmvjeA18b7VkuZaGhQjiOHVwvsnR/HRmezu4ChPBniYgvG1pA9L46OVeiU9HSTf+zQre5TDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-11T21:27:22.814025Z","bundle_sha256":"a3a65a6c5593f578f7a56648d76959ba46ab529f76e41dfe019cea66b1cfdf75"}}