{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:IU4MBV5Y5V6HYCDFGJCQT3OJTE","short_pith_number":"pith:IU4MBV5Y","canonical_record":{"source":{"id":"1707.01216","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2017-07-05T05:25:56Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"020f66be9811a3a587bbab4cf5ec8924af0f2d04af7b16a9f1a72674d437a46a","abstract_canon_sha256":"cd985b595dbc5346df89e187b4716994da6b3d123a78d0e0ae5259cc77660478"},"schema_version":"1.0"},"canonical_sha256":"4538c0d7b8ed7c7c0865324509edc99914cb4549a352a2fc2f1e3691f57610e9","source":{"kind":"arxiv","id":"1707.01216","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1707.01216","created_at":"2026-05-18T00:02:13Z"},{"alias_kind":"arxiv_version","alias_value":"1707.01216v2","created_at":"2026-05-18T00:02:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1707.01216","created_at":"2026-05-18T00:02:13Z"},{"alias_kind":"pith_short_12","alias_value":"IU4MBV5Y5V6H","created_at":"2026-05-18T12:31:21Z"},{"alias_kind":"pith_short_16","alias_value":"IU4MBV5Y5V6HYCDF","created_at":"2026-05-18T12:31:21Z"},{"alias_kind":"pith_short_8","alias_value":"IU4MBV5Y","created_at":"2026-05-18T12:31:21Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:IU4MBV5Y5V6HYCDFGJCQT3OJTE","target":"record","payload":{"canonical_record":{"source":{"id":"1707.01216","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2017-07-05T05:25:56Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"020f66be9811a3a587bbab4cf5ec8924af0f2d04af7b16a9f1a72674d437a46a","abstract_canon_sha256":"cd985b595dbc5346df89e187b4716994da6b3d123a78d0e0ae5259cc77660478"},"schema_version":"1.0"},"canonical_sha256":"4538c0d7b8ed7c7c0865324509edc99914cb4549a352a2fc2f1e3691f57610e9","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:02:13.477221Z","signature_b64":"pghATCagcXPzvGUY05KPq+T+ozl7N02n9bYUtOlR0JjucnyqYgC1bVleTaSE5Fd3ZpbpQJJUIvz4FBVQ8AG/AA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4538c0d7b8ed7c7c0865324509edc99914cb4549a352a2fc2f1e3691f57610e9","last_reissued_at":"2026-05-18T00:02:13.476600Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:02:13.476600Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1707.01216","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":"2026-05-18T00:02:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"T4fDeUWJCR4D91ng3Zb3U6Iy1wnjkhgtHzH6yBQJSABBdBDmHcsW+BdJYDE19697BrF4YQC2TOOCcWfpjnvIDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T14:36:38.725081Z"},"content_sha256":"32036b84531a0124ce2275b0e624019f1a846fd1119ba9cb0ffa370c7708d495","schema_version":"1.0","event_id":"sha256:32036b84531a0124ce2275b0e624019f1a846fd1119ba9cb0ffa370c7708d495"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:IU4MBV5Y5V6HYCDFGJCQT3OJTE","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Mustafin varieties, moduli spaces and tropical geometry","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.AG","authors_text":"Binglin Li, Marvin Anas Hahn","submitted_at":"2017-07-05T05:25:56Z","abstract_excerpt":"Mustafin varieties are flat degenerations of projective spaces, induced by a choice of an $n-$tuple of lattices in a vector space over a non-archimedean field. They were introduced by Mustafin in the 70s in order to generalise Mumford's groundbreaking work on the unformisation of curves to higher dimension. These varieties have a rich combinatorial structure as can be seen in pioneering work of Cartwright, H\\\"abich, Sturmfels and Werner. In this paper, we introduce a new approach to Mustafin varieties in terms of images of rational maps, which were studied by Li. Applying tropical intersection"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.01216","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":"2026-05-18T00:02:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"t1TjawRmFxRlJNHgjE+BqP0HAxZEcuitGrl8lizxlA/RkFcAwex5qu1QiYoAoOf9v/Xf23BDme+HAaR4CJjxDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T14:36:38.725450Z"},"content_sha256":"f2a67ed0e6bc20bd7fd5118cf56e9a51f54c42778a9523d1600aac4d58ddab66","schema_version":"1.0","event_id":"sha256:f2a67ed0e6bc20bd7fd5118cf56e9a51f54c42778a9523d1600aac4d58ddab66"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/IU4MBV5Y5V6HYCDFGJCQT3OJTE/bundle.json","state_url":"https://pith.science/pith/IU4MBV5Y5V6HYCDFGJCQT3OJTE/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/IU4MBV5Y5V6HYCDFGJCQT3OJTE/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":"2026-06-02T14:36:38Z","links":{"resolver":"https://pith.science/pith/IU4MBV5Y5V6HYCDFGJCQT3OJTE","bundle":"https://pith.science/pith/IU4MBV5Y5V6HYCDFGJCQT3OJTE/bundle.json","state":"https://pith.science/pith/IU4MBV5Y5V6HYCDFGJCQT3OJTE/state.json","well_known_bundle":"https://pith.science/.well-known/pith/IU4MBV5Y5V6HYCDFGJCQT3OJTE/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:IU4MBV5Y5V6HYCDFGJCQT3OJTE","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":"cd985b595dbc5346df89e187b4716994da6b3d123a78d0e0ae5259cc77660478","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2017-07-05T05:25:56Z","title_canon_sha256":"020f66be9811a3a587bbab4cf5ec8924af0f2d04af7b16a9f1a72674d437a46a"},"schema_version":"1.0","source":{"id":"1707.01216","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1707.01216","created_at":"2026-05-18T00:02:13Z"},{"alias_kind":"arxiv_version","alias_value":"1707.01216v2","created_at":"2026-05-18T00:02:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1707.01216","created_at":"2026-05-18T00:02:13Z"},{"alias_kind":"pith_short_12","alias_value":"IU4MBV5Y5V6H","created_at":"2026-05-18T12:31:21Z"},{"alias_kind":"pith_short_16","alias_value":"IU4MBV5Y5V6HYCDF","created_at":"2026-05-18T12:31:21Z"},{"alias_kind":"pith_short_8","alias_value":"IU4MBV5Y","created_at":"2026-05-18T12:31:21Z"}],"graph_snapshots":[{"event_id":"sha256:f2a67ed0e6bc20bd7fd5118cf56e9a51f54c42778a9523d1600aac4d58ddab66","target":"graph","created_at":"2026-05-18T00:02:13Z","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":"Mustafin varieties are flat degenerations of projective spaces, induced by a choice of an $n-$tuple of lattices in a vector space over a non-archimedean field. They were introduced by Mustafin in the 70s in order to generalise Mumford's groundbreaking work on the unformisation of curves to higher dimension. These varieties have a rich combinatorial structure as can be seen in pioneering work of Cartwright, H\\\"abich, Sturmfels and Werner. In this paper, we introduce a new approach to Mustafin varieties in terms of images of rational maps, which were studied by Li. Applying tropical intersection","authors_text":"Binglin Li, Marvin Anas Hahn","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2017-07-05T05:25:56Z","title":"Mustafin varieties, moduli spaces and tropical geometry"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.01216","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":"sha256:32036b84531a0124ce2275b0e624019f1a846fd1119ba9cb0ffa370c7708d495","target":"record","created_at":"2026-05-18T00:02:13Z","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":"cd985b595dbc5346df89e187b4716994da6b3d123a78d0e0ae5259cc77660478","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2017-07-05T05:25:56Z","title_canon_sha256":"020f66be9811a3a587bbab4cf5ec8924af0f2d04af7b16a9f1a72674d437a46a"},"schema_version":"1.0","source":{"id":"1707.01216","kind":"arxiv","version":2}},"canonical_sha256":"4538c0d7b8ed7c7c0865324509edc99914cb4549a352a2fc2f1e3691f57610e9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4538c0d7b8ed7c7c0865324509edc99914cb4549a352a2fc2f1e3691f57610e9","first_computed_at":"2026-05-18T00:02:13.476600Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:02:13.476600Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"pghATCagcXPzvGUY05KPq+T+ozl7N02n9bYUtOlR0JjucnyqYgC1bVleTaSE5Fd3ZpbpQJJUIvz4FBVQ8AG/AA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:02:13.477221Z","signed_message":"canonical_sha256_bytes"},"source_id":"1707.01216","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:32036b84531a0124ce2275b0e624019f1a846fd1119ba9cb0ffa370c7708d495","sha256:f2a67ed0e6bc20bd7fd5118cf56e9a51f54c42778a9523d1600aac4d58ddab66"],"state_sha256":"ef61b62fa39c3c53c0fb69d282c01a5139cf72f0b98dd1c6d3d5bd88aaf75a08"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mwaPf5Aw2Z69WXVPoB+mt+glIwt6CvZjGc5Gt5jk6vvvWB3if4dg+Igltt4JIzmBag+9PJ2cpj1NvCS++j7JDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T14:36:38.727409Z","bundle_sha256":"ed427fae58c5c7876653750adb7ce8f355986f254fc0daa888e618316c9d7426"}}