{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:UXYP3DCWWDDBT26DVEQQL5TRIA","short_pith_number":"pith:UXYP3DCW","canonical_record":{"source":{"id":"1507.07071","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2015-07-25T05:53:09Z","cross_cats_sorted":[],"title_canon_sha256":"6826d33fbb458fafb3c13fb7c1c88ce3358ce663b9f9b7d06cefd1780972b974","abstract_canon_sha256":"c2765081b0c17d5deb63ccf05252ebf6ddcf9c0a3503bb0f4609f4605814a703"},"schema_version":"1.0"},"canonical_sha256":"a5f0fd8c56b0c619ebc3a92105f67140111b2f1143847c25d401eda3b518f6fe","source":{"kind":"arxiv","id":"1507.07071","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1507.07071","created_at":"2026-05-18T01:36:17Z"},{"alias_kind":"arxiv_version","alias_value":"1507.07071v1","created_at":"2026-05-18T01:36:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.07071","created_at":"2026-05-18T01:36:17Z"},{"alias_kind":"pith_short_12","alias_value":"UXYP3DCWWDDB","created_at":"2026-05-18T12:29:44Z"},{"alias_kind":"pith_short_16","alias_value":"UXYP3DCWWDDBT26D","created_at":"2026-05-18T12:29:44Z"},{"alias_kind":"pith_short_8","alias_value":"UXYP3DCW","created_at":"2026-05-18T12:29:44Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:UXYP3DCWWDDBT26DVEQQL5TRIA","target":"record","payload":{"canonical_record":{"source":{"id":"1507.07071","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2015-07-25T05:53:09Z","cross_cats_sorted":[],"title_canon_sha256":"6826d33fbb458fafb3c13fb7c1c88ce3358ce663b9f9b7d06cefd1780972b974","abstract_canon_sha256":"c2765081b0c17d5deb63ccf05252ebf6ddcf9c0a3503bb0f4609f4605814a703"},"schema_version":"1.0"},"canonical_sha256":"a5f0fd8c56b0c619ebc3a92105f67140111b2f1143847c25d401eda3b518f6fe","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:36:17.320283Z","signature_b64":"FmXBtiyDd+octHmu9HEXgHemDZyomnu06htLH6fEuKKRvWEO26Mmor2eVmtoES1TmpaHvMwulkEiU9Oa5QE7DA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a5f0fd8c56b0c619ebc3a92105f67140111b2f1143847c25d401eda3b518f6fe","last_reissued_at":"2026-05-18T01:36:17.319685Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:36:17.319685Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1507.07071","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":"2026-05-18T01:36:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2O2snZDXgwoEykKSN2Z5uCjuVI4e7Glx88yb1NUEXX87Ybt6SphR4IW/SjQEfPhCbnhMABCfnmmwEDABlzcsCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T19:14:43.742866Z"},"content_sha256":"5275ba2228f74baee61db517bc11f364803ba05155517dbd43238689139fdd11","schema_version":"1.0","event_id":"sha256:5275ba2228f74baee61db517bc11f364803ba05155517dbd43238689139fdd11"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:UXYP3DCWWDDBT26DVEQQL5TRIA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Equilibrium triangulations of some quasitoric 4-manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Basudeb Datta, Soumen Sarkar","submitted_at":"2015-07-25T05:53:09Z","abstract_excerpt":"Quasitoric manifolds, introduced by M. Davis and T. Januskiewicz in 1991, are topological generalizations of smooth complex projective spaces. In 1992, Banchoff and K\\\"uhnel constructed a 10-vertex equilibrium triangulations of $\\CP^2$. We generalize this construction for quasitoric manifolds and construct some equilibrium triangulations of $4$-dimensional quasitoric manifolds. In some cases, our constructions give vertex minimal equilibrium triangulations."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.07071","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":"2026-05-18T01:36:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LGN6PqceYBUbUrKlymy2bJqholGk7Q7MJsjyhah+lv5MI+BfLPEI0GBy1C/xJolGpbCMu8KJJ91pUUhpzlSiAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T19:14:43.743525Z"},"content_sha256":"5e503071c0325d6d8a785554f5c0c71e0e3e010d37163d9f064a543bea20cb60","schema_version":"1.0","event_id":"sha256:5e503071c0325d6d8a785554f5c0c71e0e3e010d37163d9f064a543bea20cb60"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/UXYP3DCWWDDBT26DVEQQL5TRIA/bundle.json","state_url":"https://pith.science/pith/UXYP3DCWWDDBT26DVEQQL5TRIA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/UXYP3DCWWDDBT26DVEQQL5TRIA/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":"2026-05-25T19:14:43Z","links":{"resolver":"https://pith.science/pith/UXYP3DCWWDDBT26DVEQQL5TRIA","bundle":"https://pith.science/pith/UXYP3DCWWDDBT26DVEQQL5TRIA/bundle.json","state":"https://pith.science/pith/UXYP3DCWWDDBT26DVEQQL5TRIA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/UXYP3DCWWDDBT26DVEQQL5TRIA/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:UXYP3DCWWDDBT26DVEQQL5TRIA","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":"c2765081b0c17d5deb63ccf05252ebf6ddcf9c0a3503bb0f4609f4605814a703","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2015-07-25T05:53:09Z","title_canon_sha256":"6826d33fbb458fafb3c13fb7c1c88ce3358ce663b9f9b7d06cefd1780972b974"},"schema_version":"1.0","source":{"id":"1507.07071","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1507.07071","created_at":"2026-05-18T01:36:17Z"},{"alias_kind":"arxiv_version","alias_value":"1507.07071v1","created_at":"2026-05-18T01:36:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.07071","created_at":"2026-05-18T01:36:17Z"},{"alias_kind":"pith_short_12","alias_value":"UXYP3DCWWDDB","created_at":"2026-05-18T12:29:44Z"},{"alias_kind":"pith_short_16","alias_value":"UXYP3DCWWDDBT26D","created_at":"2026-05-18T12:29:44Z"},{"alias_kind":"pith_short_8","alias_value":"UXYP3DCW","created_at":"2026-05-18T12:29:44Z"}],"graph_snapshots":[{"event_id":"sha256:5e503071c0325d6d8a785554f5c0c71e0e3e010d37163d9f064a543bea20cb60","target":"graph","created_at":"2026-05-18T01:36:17Z","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":"Quasitoric manifolds, introduced by M. Davis and T. Januskiewicz in 1991, are topological generalizations of smooth complex projective spaces. In 1992, Banchoff and K\\\"uhnel constructed a 10-vertex equilibrium triangulations of $\\CP^2$. We generalize this construction for quasitoric manifolds and construct some equilibrium triangulations of $4$-dimensional quasitoric manifolds. In some cases, our constructions give vertex minimal equilibrium triangulations.","authors_text":"Basudeb Datta, Soumen Sarkar","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2015-07-25T05:53:09Z","title":"Equilibrium triangulations of some quasitoric 4-manifolds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.07071","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":"sha256:5275ba2228f74baee61db517bc11f364803ba05155517dbd43238689139fdd11","target":"record","created_at":"2026-05-18T01:36:17Z","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":"c2765081b0c17d5deb63ccf05252ebf6ddcf9c0a3503bb0f4609f4605814a703","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2015-07-25T05:53:09Z","title_canon_sha256":"6826d33fbb458fafb3c13fb7c1c88ce3358ce663b9f9b7d06cefd1780972b974"},"schema_version":"1.0","source":{"id":"1507.07071","kind":"arxiv","version":1}},"canonical_sha256":"a5f0fd8c56b0c619ebc3a92105f67140111b2f1143847c25d401eda3b518f6fe","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a5f0fd8c56b0c619ebc3a92105f67140111b2f1143847c25d401eda3b518f6fe","first_computed_at":"2026-05-18T01:36:17.319685Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:36:17.319685Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"FmXBtiyDd+octHmu9HEXgHemDZyomnu06htLH6fEuKKRvWEO26Mmor2eVmtoES1TmpaHvMwulkEiU9Oa5QE7DA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:36:17.320283Z","signed_message":"canonical_sha256_bytes"},"source_id":"1507.07071","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5275ba2228f74baee61db517bc11f364803ba05155517dbd43238689139fdd11","sha256:5e503071c0325d6d8a785554f5c0c71e0e3e010d37163d9f064a543bea20cb60"],"state_sha256":"b6724db39530c25bc980c4c9542f96834b15b36f34bc8ea298d0c3560c1b6954"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IgaQKBl/TJzfdywcVCzAY23roiLVQ2bASMgHQhysIcMxotKP4uMfngvDI2KZo+VkN+XlHkAjBq/mMSwdAkMKDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-25T19:14:43.747132Z","bundle_sha256":"84b5ff05eca5afb4ea9815e350b1ea197bc584c86643d92517ca36c7f5e0bee6"}}