{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:B2JKYMYSVWBECEIOPTDKE7N7JN","short_pith_number":"pith:B2JKYMYS","canonical_record":{"source":{"id":"1804.04305","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2018-04-12T03:45:12Z","cross_cats_sorted":["math.MP","nlin.SI"],"title_canon_sha256":"886a80d6668bf5723511ff325190eb52d8d5497815a87759ccd4cddd452d29c5","abstract_canon_sha256":"2edc50946340395d5594d8a8d4300050b0d9cb5c7eedf53026bdb16c5964348c"},"schema_version":"1.0"},"canonical_sha256":"0e92ac3312ad8241110e7cc6a27dbf4b50e733d66b589e9d90a51fd3b08c54bf","source":{"kind":"arxiv","id":"1804.04305","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1804.04305","created_at":"2026-05-18T00:11:56Z"},{"alias_kind":"arxiv_version","alias_value":"1804.04305v2","created_at":"2026-05-18T00:11:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1804.04305","created_at":"2026-05-18T00:11:56Z"},{"alias_kind":"pith_short_12","alias_value":"B2JKYMYSVWBE","created_at":"2026-05-18T12:32:13Z"},{"alias_kind":"pith_short_16","alias_value":"B2JKYMYSVWBECEIO","created_at":"2026-05-18T12:32:13Z"},{"alias_kind":"pith_short_8","alias_value":"B2JKYMYS","created_at":"2026-05-18T12:32:13Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:B2JKYMYSVWBECEIOPTDKE7N7JN","target":"record","payload":{"canonical_record":{"source":{"id":"1804.04305","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2018-04-12T03:45:12Z","cross_cats_sorted":["math.MP","nlin.SI"],"title_canon_sha256":"886a80d6668bf5723511ff325190eb52d8d5497815a87759ccd4cddd452d29c5","abstract_canon_sha256":"2edc50946340395d5594d8a8d4300050b0d9cb5c7eedf53026bdb16c5964348c"},"schema_version":"1.0"},"canonical_sha256":"0e92ac3312ad8241110e7cc6a27dbf4b50e733d66b589e9d90a51fd3b08c54bf","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:11:56.999162Z","signature_b64":"b+sxnnV0XHbpA4iU3IgGPtGj7QPo8mbnKNvvXDNCyEhCNJSq6PMqV4fgUdKMh4e+uouAMnQVMMCpgLCCcgcSAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0e92ac3312ad8241110e7cc6a27dbf4b50e733d66b589e9d90a51fd3b08c54bf","last_reissued_at":"2026-05-18T00:11:56.998634Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:11:56.998634Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1804.04305","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":"2026-05-18T00:11:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2QnuqWKEIahz0XYlMF12bHZ5il9zXXkohnBfNAjKt52HD2LBlf8T+XW9FIy8TZVLncBprHC0GjzF3+YviA6+AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T02:13:47.697960Z"},"content_sha256":"a800530031247e6f4a93b0b4c42ed66076deccb26ec308baeee024b35127ae50","schema_version":"1.0","event_id":"sha256:a800530031247e6f4a93b0b4c42ed66076deccb26ec308baeee024b35127ae50"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:B2JKYMYSVWBECEIOPTDKE7N7JN","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Matrix product solutions to the $G_2$ reflection equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP","nlin.SI"],"primary_cat":"math-ph","authors_text":"Atsuo Kuniba","submitted_at":"2018-04-12T03:45:12Z","abstract_excerpt":"We study the $G_2$ reflection equation for the three particles in $1+1$ dimension that undergo a special scattering/reflections described by the Pappus theorem. It is a sixth order equation and serves as a natural $G_2$ analogue of the Yang-Baxter and the reflection equations corresponding to the cubic and the quartic Coxeter relations of type $A$ and $BC$, respectively. We construct matrix product solutions to the $G_2$ reflection equation by exploiting a connection to the representation theory of the quantized coordinate ring $A_q(G_2)$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.04305","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":"2026-05-18T00:11:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"z1V19eZvFbgEppok0Y2vQXluJWWCtS66uZiXRqxJV0HS/v3ccPdOv2cIeCJ6EoHeRIrosqT1RV0GPifa3qAXAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T02:13:47.698783Z"},"content_sha256":"ea8c56f911ca2a628eed476554c2f0ace73babac415213e1d8497da7985063b8","schema_version":"1.0","event_id":"sha256:ea8c56f911ca2a628eed476554c2f0ace73babac415213e1d8497da7985063b8"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/B2JKYMYSVWBECEIOPTDKE7N7JN/bundle.json","state_url":"https://pith.science/pith/B2JKYMYSVWBECEIOPTDKE7N7JN/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/B2JKYMYSVWBECEIOPTDKE7N7JN/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":"2026-06-08T02:13:47Z","links":{"resolver":"https://pith.science/pith/B2JKYMYSVWBECEIOPTDKE7N7JN","bundle":"https://pith.science/pith/B2JKYMYSVWBECEIOPTDKE7N7JN/bundle.json","state":"https://pith.science/pith/B2JKYMYSVWBECEIOPTDKE7N7JN/state.json","well_known_bundle":"https://pith.science/.well-known/pith/B2JKYMYSVWBECEIOPTDKE7N7JN/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:B2JKYMYSVWBECEIOPTDKE7N7JN","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":"2edc50946340395d5594d8a8d4300050b0d9cb5c7eedf53026bdb16c5964348c","cross_cats_sorted":["math.MP","nlin.SI"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2018-04-12T03:45:12Z","title_canon_sha256":"886a80d6668bf5723511ff325190eb52d8d5497815a87759ccd4cddd452d29c5"},"schema_version":"1.0","source":{"id":"1804.04305","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1804.04305","created_at":"2026-05-18T00:11:56Z"},{"alias_kind":"arxiv_version","alias_value":"1804.04305v2","created_at":"2026-05-18T00:11:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1804.04305","created_at":"2026-05-18T00:11:56Z"},{"alias_kind":"pith_short_12","alias_value":"B2JKYMYSVWBE","created_at":"2026-05-18T12:32:13Z"},{"alias_kind":"pith_short_16","alias_value":"B2JKYMYSVWBECEIO","created_at":"2026-05-18T12:32:13Z"},{"alias_kind":"pith_short_8","alias_value":"B2JKYMYS","created_at":"2026-05-18T12:32:13Z"}],"graph_snapshots":[{"event_id":"sha256:ea8c56f911ca2a628eed476554c2f0ace73babac415213e1d8497da7985063b8","target":"graph","created_at":"2026-05-18T00:11:56Z","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 study the $G_2$ reflection equation for the three particles in $1+1$ dimension that undergo a special scattering/reflections described by the Pappus theorem. It is a sixth order equation and serves as a natural $G_2$ analogue of the Yang-Baxter and the reflection equations corresponding to the cubic and the quartic Coxeter relations of type $A$ and $BC$, respectively. We construct matrix product solutions to the $G_2$ reflection equation by exploiting a connection to the representation theory of the quantized coordinate ring $A_q(G_2)$.","authors_text":"Atsuo Kuniba","cross_cats":["math.MP","nlin.SI"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2018-04-12T03:45:12Z","title":"Matrix product solutions to the $G_2$ reflection equation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.04305","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:a800530031247e6f4a93b0b4c42ed66076deccb26ec308baeee024b35127ae50","target":"record","created_at":"2026-05-18T00:11:56Z","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":"2edc50946340395d5594d8a8d4300050b0d9cb5c7eedf53026bdb16c5964348c","cross_cats_sorted":["math.MP","nlin.SI"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2018-04-12T03:45:12Z","title_canon_sha256":"886a80d6668bf5723511ff325190eb52d8d5497815a87759ccd4cddd452d29c5"},"schema_version":"1.0","source":{"id":"1804.04305","kind":"arxiv","version":2}},"canonical_sha256":"0e92ac3312ad8241110e7cc6a27dbf4b50e733d66b589e9d90a51fd3b08c54bf","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0e92ac3312ad8241110e7cc6a27dbf4b50e733d66b589e9d90a51fd3b08c54bf","first_computed_at":"2026-05-18T00:11:56.998634Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:11:56.998634Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"b+sxnnV0XHbpA4iU3IgGPtGj7QPo8mbnKNvvXDNCyEhCNJSq6PMqV4fgUdKMh4e+uouAMnQVMMCpgLCCcgcSAg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:11:56.999162Z","signed_message":"canonical_sha256_bytes"},"source_id":"1804.04305","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a800530031247e6f4a93b0b4c42ed66076deccb26ec308baeee024b35127ae50","sha256:ea8c56f911ca2a628eed476554c2f0ace73babac415213e1d8497da7985063b8"],"state_sha256":"49aeca048d5ec746551e257e9caf34e775706748cf232cf3de97a5a6d1e9e559"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"24uNgER7B6l+JWWqhgLoERC/EHh5fpHH+aNCTpZ9rkx6md3kLTR+n+7556O6XudrgvyxnE2Q+caAZvYIBy7sDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-08T02:13:47.702515Z","bundle_sha256":"faa404e62f166495b6732333e6fde7e38bf37a4adf3b0ca3a195b5cecc29fb84"}}