{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:DGSQ2Z6JI3ZARA2SSRGTVHQB5E","short_pith_number":"pith:DGSQ2Z6J","canonical_record":{"source":{"id":"1410.8112","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-10-29T19:32:46Z","cross_cats_sorted":[],"title_canon_sha256":"e594e390af8cea8df33bd738992cac7c1101652b1a060268feefdf4abd4974b1","abstract_canon_sha256":"dc67223c1561801c6aa07b6b40ed5db57b532962970f057bcc3bae0456e599b1"},"schema_version":"1.0"},"canonical_sha256":"19a50d67c946f2088352944d3a9e01e92463f8886967409da4bf1c623747fb4f","source":{"kind":"arxiv","id":"1410.8112","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1410.8112","created_at":"2026-05-18T01:36:41Z"},{"alias_kind":"arxiv_version","alias_value":"1410.8112v3","created_at":"2026-05-18T01:36:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1410.8112","created_at":"2026-05-18T01:36:41Z"},{"alias_kind":"pith_short_12","alias_value":"DGSQ2Z6JI3ZA","created_at":"2026-05-18T12:28:25Z"},{"alias_kind":"pith_short_16","alias_value":"DGSQ2Z6JI3ZARA2S","created_at":"2026-05-18T12:28:25Z"},{"alias_kind":"pith_short_8","alias_value":"DGSQ2Z6J","created_at":"2026-05-18T12:28:25Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:DGSQ2Z6JI3ZARA2SSRGTVHQB5E","target":"record","payload":{"canonical_record":{"source":{"id":"1410.8112","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-10-29T19:32:46Z","cross_cats_sorted":[],"title_canon_sha256":"e594e390af8cea8df33bd738992cac7c1101652b1a060268feefdf4abd4974b1","abstract_canon_sha256":"dc67223c1561801c6aa07b6b40ed5db57b532962970f057bcc3bae0456e599b1"},"schema_version":"1.0"},"canonical_sha256":"19a50d67c946f2088352944d3a9e01e92463f8886967409da4bf1c623747fb4f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:36:41.678075Z","signature_b64":"x7q4sEjIo6GYA2by11+eula9TCuySntV1twyYy+S46eKxgRQICvvEpoiZj8SlUvpDa2KXng+grfEq0a21huxCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"19a50d67c946f2088352944d3a9e01e92463f8886967409da4bf1c623747fb4f","last_reissued_at":"2026-05-18T01:36:41.677521Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:36:41.677521Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1410.8112","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":"2026-05-18T01:36:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Y+XblkYvoucWb6o/oINJpr06YboNcKLTfPVio7Guix1Vy0diePTwdEIM8cKQT06TsrUg/tZ6lKmfzPB0pCLDAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T06:40:31.761612Z"},"content_sha256":"070f8c84a24855be8bccd6451a6a9132f44b43fad890a670613887abc29ce65b","schema_version":"1.0","event_id":"sha256:070f8c84a24855be8bccd6451a6a9132f44b43fad890a670613887abc29ce65b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:DGSQ2Z6JI3ZARA2SSRGTVHQB5E","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A note on a 2-enumeration of antisymmetric monotone triangles","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Tri Lai","submitted_at":"2014-10-29T19:32:46Z","abstract_excerpt":"In their unpublished work, Jockusch and Propp showed that a 2-enumeration of antisymmetric monotone triangles is given by a simple product formula. On the other hand, the author proved that the same formula counts the domino tilings of the quartered Aztec rectangle. In this paper, we explain this phenomenon directly by building a correspondence between the antisymmetric monotone triangles and domino tilings of the quartered Aztec rectangle."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.8112","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":"2026-05-18T01:36:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QbVruJl6QKqN3P55L1mJKiQZ1NLPjxjD92lAy/Itf0iampAVc1LQ9e1DuiKZ6SelH8CkyGttc7Gzo2GpX2eUDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T06:40:31.761961Z"},"content_sha256":"46cfa52d48ff9d5f9749a20bfa20c41ca5dc24316d9ea3a9b20bd2ad933e6c50","schema_version":"1.0","event_id":"sha256:46cfa52d48ff9d5f9749a20bfa20c41ca5dc24316d9ea3a9b20bd2ad933e6c50"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/DGSQ2Z6JI3ZARA2SSRGTVHQB5E/bundle.json","state_url":"https://pith.science/pith/DGSQ2Z6JI3ZARA2SSRGTVHQB5E/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/DGSQ2Z6JI3ZARA2SSRGTVHQB5E/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":"2026-06-23T06:40:31Z","links":{"resolver":"https://pith.science/pith/DGSQ2Z6JI3ZARA2SSRGTVHQB5E","bundle":"https://pith.science/pith/DGSQ2Z6JI3ZARA2SSRGTVHQB5E/bundle.json","state":"https://pith.science/pith/DGSQ2Z6JI3ZARA2SSRGTVHQB5E/state.json","well_known_bundle":"https://pith.science/.well-known/pith/DGSQ2Z6JI3ZARA2SSRGTVHQB5E/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:DGSQ2Z6JI3ZARA2SSRGTVHQB5E","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":"dc67223c1561801c6aa07b6b40ed5db57b532962970f057bcc3bae0456e599b1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-10-29T19:32:46Z","title_canon_sha256":"e594e390af8cea8df33bd738992cac7c1101652b1a060268feefdf4abd4974b1"},"schema_version":"1.0","source":{"id":"1410.8112","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1410.8112","created_at":"2026-05-18T01:36:41Z"},{"alias_kind":"arxiv_version","alias_value":"1410.8112v3","created_at":"2026-05-18T01:36:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1410.8112","created_at":"2026-05-18T01:36:41Z"},{"alias_kind":"pith_short_12","alias_value":"DGSQ2Z6JI3ZA","created_at":"2026-05-18T12:28:25Z"},{"alias_kind":"pith_short_16","alias_value":"DGSQ2Z6JI3ZARA2S","created_at":"2026-05-18T12:28:25Z"},{"alias_kind":"pith_short_8","alias_value":"DGSQ2Z6J","created_at":"2026-05-18T12:28:25Z"}],"graph_snapshots":[{"event_id":"sha256:46cfa52d48ff9d5f9749a20bfa20c41ca5dc24316d9ea3a9b20bd2ad933e6c50","target":"graph","created_at":"2026-05-18T01:36:41Z","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 their unpublished work, Jockusch and Propp showed that a 2-enumeration of antisymmetric monotone triangles is given by a simple product formula. On the other hand, the author proved that the same formula counts the domino tilings of the quartered Aztec rectangle. In this paper, we explain this phenomenon directly by building a correspondence between the antisymmetric monotone triangles and domino tilings of the quartered Aztec rectangle.","authors_text":"Tri Lai","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-10-29T19:32:46Z","title":"A note on a 2-enumeration of antisymmetric monotone triangles"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.8112","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":"sha256:070f8c84a24855be8bccd6451a6a9132f44b43fad890a670613887abc29ce65b","target":"record","created_at":"2026-05-18T01:36:41Z","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":"dc67223c1561801c6aa07b6b40ed5db57b532962970f057bcc3bae0456e599b1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-10-29T19:32:46Z","title_canon_sha256":"e594e390af8cea8df33bd738992cac7c1101652b1a060268feefdf4abd4974b1"},"schema_version":"1.0","source":{"id":"1410.8112","kind":"arxiv","version":3}},"canonical_sha256":"19a50d67c946f2088352944d3a9e01e92463f8886967409da4bf1c623747fb4f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"19a50d67c946f2088352944d3a9e01e92463f8886967409da4bf1c623747fb4f","first_computed_at":"2026-05-18T01:36:41.677521Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:36:41.677521Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"x7q4sEjIo6GYA2by11+eula9TCuySntV1twyYy+S46eKxgRQICvvEpoiZj8SlUvpDa2KXng+grfEq0a21huxCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:36:41.678075Z","signed_message":"canonical_sha256_bytes"},"source_id":"1410.8112","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:070f8c84a24855be8bccd6451a6a9132f44b43fad890a670613887abc29ce65b","sha256:46cfa52d48ff9d5f9749a20bfa20c41ca5dc24316d9ea3a9b20bd2ad933e6c50"],"state_sha256":"67f77b9abcb04dd10af142987f1f819e8bc89435be15de8b297a220b87e99728"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5IwUAcrz6uaMQrPUP5HYgU/7AGuFHvmaUtXim5WT8AR+RtJ7udeR1T8EsnOFTRR82oAmd1rqO923eO55qFBpBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T06:40:31.763981Z","bundle_sha256":"a2369183174f563f06eac307e5f0149cb153b821a9ca79e1dd429ccfe285c128"}}