{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:4MXQMSXDOAKEJVQZQBMQKUHZYP","short_pith_number":"pith:4MXQMSXD","canonical_record":{"source":{"id":"1805.09280","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-05-23T16:52:28Z","cross_cats_sorted":[],"title_canon_sha256":"0afa8fb362f3a0cb04f0ec037366293ebb8595b06479acf038024072bda6e2ed","abstract_canon_sha256":"db93a2dc4c3110742f8b4fd62013269af3751fbe8970b3c29525fee7cb9a28e9"},"schema_version":"1.0"},"canonical_sha256":"e32f064ae3701444d61980590550f9c3d2bb22437e954621e3711408634441c2","source":{"kind":"arxiv","id":"1805.09280","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1805.09280","created_at":"2026-05-17T23:47:31Z"},{"alias_kind":"arxiv_version","alias_value":"1805.09280v3","created_at":"2026-05-17T23:47:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1805.09280","created_at":"2026-05-17T23:47:31Z"},{"alias_kind":"pith_short_12","alias_value":"4MXQMSXDOAKE","created_at":"2026-05-18T12:32:05Z"},{"alias_kind":"pith_short_16","alias_value":"4MXQMSXDOAKEJVQZ","created_at":"2026-05-18T12:32:05Z"},{"alias_kind":"pith_short_8","alias_value":"4MXQMSXD","created_at":"2026-05-18T12:32:05Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:4MXQMSXDOAKEJVQZQBMQKUHZYP","target":"record","payload":{"canonical_record":{"source":{"id":"1805.09280","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-05-23T16:52:28Z","cross_cats_sorted":[],"title_canon_sha256":"0afa8fb362f3a0cb04f0ec037366293ebb8595b06479acf038024072bda6e2ed","abstract_canon_sha256":"db93a2dc4c3110742f8b4fd62013269af3751fbe8970b3c29525fee7cb9a28e9"},"schema_version":"1.0"},"canonical_sha256":"e32f064ae3701444d61980590550f9c3d2bb22437e954621e3711408634441c2","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:47:31.075019Z","signature_b64":"Np1WDWcDTsvKIUild+aUOG4O2hqFUNREikFyhpD1tVbjtgkkH6bgQ+qwtSDO2TF5YBr7Ncc2Ef9lP5RrZ6SVCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e32f064ae3701444d61980590550f9c3d2bb22437e954621e3711408634441c2","last_reissued_at":"2026-05-17T23:47:31.074559Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:47:31.074559Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1805.09280","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":"2026-05-17T23:47:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/3lfHFhED/vEwMAV6F5JArxXBwuUutIdl7Fpy5FoR0166U1p1XQzD7dEhy5YkP7M33znUfYJVtT61GJQ48z0Bw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T03:06:16.477000Z"},"content_sha256":"0b082b9111b1cfefd3358f85ffbcaa14ca34f6a4bd49b159b341e6d0758938b3","schema_version":"1.0","event_id":"sha256:0b082b9111b1cfefd3358f85ffbcaa14ca34f6a4bd49b159b341e6d0758938b3"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:4MXQMSXDOAKEJVQZQBMQKUHZYP","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Dungeons and Dragons: Combinatorics for the $dP_3$ Quiver","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Gregg Musiker, Tri Lai","submitted_at":"2018-05-23T16:52:28Z","abstract_excerpt":"In this paper, we utilize the machinery of cluster algebras, quiver mutations, and brane tilings to study a variety of historical enumerative combinatorics questions all under one roof. Previous work [Zha, LMNT14], which arose during the second author's monitorship of undergraduates, and more recently of both authors [LM17], analyzed the cluster algebra associated to the cone over $\\mathbf{dP_3}$, the del Pezzo surface of degree $6$ ($\\mathbb{CP}^2$ blown up at three points). By investigating sequences of toric mutations, those occurring only at vertices with two incoming and two outgoing arro"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.09280","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":"2026-05-17T23:47:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SSMjSDX0yK3AoBLVLXoQKWgdnMYeOaQbnANQtJIS52zAiLudPtf8qxvKlR1RYx7ulxcPo0e5WkWcbKK2y2T7AA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T03:06:16.477697Z"},"content_sha256":"77d44c59c2672888e00129a540c4cb9fa936828daf95d6b36e5a52b7f42b6a2e","schema_version":"1.0","event_id":"sha256:77d44c59c2672888e00129a540c4cb9fa936828daf95d6b36e5a52b7f42b6a2e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/4MXQMSXDOAKEJVQZQBMQKUHZYP/bundle.json","state_url":"https://pith.science/pith/4MXQMSXDOAKEJVQZQBMQKUHZYP/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/4MXQMSXDOAKEJVQZQBMQKUHZYP/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":"2026-06-06T03:06:16Z","links":{"resolver":"https://pith.science/pith/4MXQMSXDOAKEJVQZQBMQKUHZYP","bundle":"https://pith.science/pith/4MXQMSXDOAKEJVQZQBMQKUHZYP/bundle.json","state":"https://pith.science/pith/4MXQMSXDOAKEJVQZQBMQKUHZYP/state.json","well_known_bundle":"https://pith.science/.well-known/pith/4MXQMSXDOAKEJVQZQBMQKUHZYP/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:4MXQMSXDOAKEJVQZQBMQKUHZYP","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":"db93a2dc4c3110742f8b4fd62013269af3751fbe8970b3c29525fee7cb9a28e9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-05-23T16:52:28Z","title_canon_sha256":"0afa8fb362f3a0cb04f0ec037366293ebb8595b06479acf038024072bda6e2ed"},"schema_version":"1.0","source":{"id":"1805.09280","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1805.09280","created_at":"2026-05-17T23:47:31Z"},{"alias_kind":"arxiv_version","alias_value":"1805.09280v3","created_at":"2026-05-17T23:47:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1805.09280","created_at":"2026-05-17T23:47:31Z"},{"alias_kind":"pith_short_12","alias_value":"4MXQMSXDOAKE","created_at":"2026-05-18T12:32:05Z"},{"alias_kind":"pith_short_16","alias_value":"4MXQMSXDOAKEJVQZ","created_at":"2026-05-18T12:32:05Z"},{"alias_kind":"pith_short_8","alias_value":"4MXQMSXD","created_at":"2026-05-18T12:32:05Z"}],"graph_snapshots":[{"event_id":"sha256:77d44c59c2672888e00129a540c4cb9fa936828daf95d6b36e5a52b7f42b6a2e","target":"graph","created_at":"2026-05-17T23:47:31Z","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 this paper, we utilize the machinery of cluster algebras, quiver mutations, and brane tilings to study a variety of historical enumerative combinatorics questions all under one roof. Previous work [Zha, LMNT14], which arose during the second author's monitorship of undergraduates, and more recently of both authors [LM17], analyzed the cluster algebra associated to the cone over $\\mathbf{dP_3}$, the del Pezzo surface of degree $6$ ($\\mathbb{CP}^2$ blown up at three points). By investigating sequences of toric mutations, those occurring only at vertices with two incoming and two outgoing arro","authors_text":"Gregg Musiker, Tri Lai","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-05-23T16:52:28Z","title":"Dungeons and Dragons: Combinatorics for the $dP_3$ Quiver"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.09280","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":"sha256:0b082b9111b1cfefd3358f85ffbcaa14ca34f6a4bd49b159b341e6d0758938b3","target":"record","created_at":"2026-05-17T23:47:31Z","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":"db93a2dc4c3110742f8b4fd62013269af3751fbe8970b3c29525fee7cb9a28e9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-05-23T16:52:28Z","title_canon_sha256":"0afa8fb362f3a0cb04f0ec037366293ebb8595b06479acf038024072bda6e2ed"},"schema_version":"1.0","source":{"id":"1805.09280","kind":"arxiv","version":3}},"canonical_sha256":"e32f064ae3701444d61980590550f9c3d2bb22437e954621e3711408634441c2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e32f064ae3701444d61980590550f9c3d2bb22437e954621e3711408634441c2","first_computed_at":"2026-05-17T23:47:31.074559Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:47:31.074559Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Np1WDWcDTsvKIUild+aUOG4O2hqFUNREikFyhpD1tVbjtgkkH6bgQ+qwtSDO2TF5YBr7Ncc2Ef9lP5RrZ6SVCQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:47:31.075019Z","signed_message":"canonical_sha256_bytes"},"source_id":"1805.09280","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0b082b9111b1cfefd3358f85ffbcaa14ca34f6a4bd49b159b341e6d0758938b3","sha256:77d44c59c2672888e00129a540c4cb9fa936828daf95d6b36e5a52b7f42b6a2e"],"state_sha256":"d7bf380e6613274d885dcf990024c008afe854dc8aa2550b55e7f2c55db2417a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"i/LGjQMK6QYwtj5BJCbdmKKG1FTFOPT5mFd74/98ZrGO2jiipYg/7JbSgX5wpTEvQ5h7PLaKIfg7QqZpCVpMDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-06T03:06:16.481298Z","bundle_sha256":"7d30d47663e11e6987e3af10d1c8c04006c9bd2461b54d558a6c9dee3268d545"}}