{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:B2KBTUL3R356TRLZNDYXST442Q","short_pith_number":"pith:B2KBTUL3","canonical_record":{"source":{"id":"1104.0407","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-04-03T17:13:54Z","cross_cats_sorted":["math.DG"],"title_canon_sha256":"53c63f8d87ea7e3db74ceb985eeae6644d7427cb63d7136b313c9090ee043a35","abstract_canon_sha256":"a9c73791a9ac84206f374f7f5578a9a1ccd5347b02a093b0381440a059d14eaa"},"schema_version":"1.0"},"canonical_sha256":"0e9419d17b8efbe9c57968f1794f9cd40c97171f366db253b7eac85f8fc786b1","source":{"kind":"arxiv","id":"1104.0407","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1104.0407","created_at":"2026-05-18T01:29:22Z"},{"alias_kind":"arxiv_version","alias_value":"1104.0407v2","created_at":"2026-05-18T01:29:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1104.0407","created_at":"2026-05-18T01:29:22Z"},{"alias_kind":"pith_short_12","alias_value":"B2KBTUL3R356","created_at":"2026-05-18T12:26:24Z"},{"alias_kind":"pith_short_16","alias_value":"B2KBTUL3R356TRLZ","created_at":"2026-05-18T12:26:24Z"},{"alias_kind":"pith_short_8","alias_value":"B2KBTUL3","created_at":"2026-05-18T12:26:24Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:B2KBTUL3R356TRLZNDYXST442Q","target":"record","payload":{"canonical_record":{"source":{"id":"1104.0407","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-04-03T17:13:54Z","cross_cats_sorted":["math.DG"],"title_canon_sha256":"53c63f8d87ea7e3db74ceb985eeae6644d7427cb63d7136b313c9090ee043a35","abstract_canon_sha256":"a9c73791a9ac84206f374f7f5578a9a1ccd5347b02a093b0381440a059d14eaa"},"schema_version":"1.0"},"canonical_sha256":"0e9419d17b8efbe9c57968f1794f9cd40c97171f366db253b7eac85f8fc786b1","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:29:22.269886Z","signature_b64":"8inPyDvkO+eviCK3vOvxVyo69adgyRBi0Jh4d8juiObnOTl9oyXUGPOie9G+k1UTMlmDixzLlcquDFYPT51TAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0e9419d17b8efbe9c57968f1794f9cd40c97171f366db253b7eac85f8fc786b1","last_reissued_at":"2026-05-18T01:29:22.269223Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:29:22.269223Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1104.0407","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":"2026-05-18T01:29:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+z9M0OL9ZvOtz+JlRu1X0vpOHXggLboUiu1DPYai3sTq1+WCoo/8e+AjZ5C2bQMFYHD896v+ZqQtLzXFWEW+CA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T22:53:37.887180Z"},"content_sha256":"db3d8f2e549cb9172de3a2d34a2c1fb8003262f88a8c1480253b3132aecfa77c","schema_version":"1.0","event_id":"sha256:db3d8f2e549cb9172de3a2d34a2c1fb8003262f88a8c1480253b3132aecfa77c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:B2KBTUL3R356TRLZNDYXST442Q","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Cluster X-varieties at infinity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.AG","authors_text":"A.B. Goncharov, V.V. Fock","submitted_at":"2011-04-03T17:13:54Z","abstract_excerpt":"A positive space is a space with a positive atlas, i.e. a collection of rational coordinate systems with subtraction free transition functions. The set of positive real points of a positive space is well defined. We define a tropical compactification of the latter. We show that it generalizes the Thurston compactification of a Teichmuller space. The tropical boundary of a positive space is a sphere with a piecewise linear structure. Cluster X-varieties are positive spaces of rather special type. We define special completions of cluster X-varieties. They have a stratification whose strata are ("},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1104.0407","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":"2026-05-18T01:29:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"o6cCcjRmU+NVv2dAPkDTUbvYikwYe8znhO2L+WhZXpFsqiEZCovRSCvwzjr9ECCwDYQZvqIkoJZNBvn01KBgAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T22:53:37.887841Z"},"content_sha256":"0d589730ce96a1f40e57424b2daf69230acaa6751daff690dcbfed75bb310cc0","schema_version":"1.0","event_id":"sha256:0d589730ce96a1f40e57424b2daf69230acaa6751daff690dcbfed75bb310cc0"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/B2KBTUL3R356TRLZNDYXST442Q/bundle.json","state_url":"https://pith.science/pith/B2KBTUL3R356TRLZNDYXST442Q/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/B2KBTUL3R356TRLZNDYXST442Q/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":"2026-05-25T22:53:37Z","links":{"resolver":"https://pith.science/pith/B2KBTUL3R356TRLZNDYXST442Q","bundle":"https://pith.science/pith/B2KBTUL3R356TRLZNDYXST442Q/bundle.json","state":"https://pith.science/pith/B2KBTUL3R356TRLZNDYXST442Q/state.json","well_known_bundle":"https://pith.science/.well-known/pith/B2KBTUL3R356TRLZNDYXST442Q/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:B2KBTUL3R356TRLZNDYXST442Q","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":"a9c73791a9ac84206f374f7f5578a9a1ccd5347b02a093b0381440a059d14eaa","cross_cats_sorted":["math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-04-03T17:13:54Z","title_canon_sha256":"53c63f8d87ea7e3db74ceb985eeae6644d7427cb63d7136b313c9090ee043a35"},"schema_version":"1.0","source":{"id":"1104.0407","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1104.0407","created_at":"2026-05-18T01:29:22Z"},{"alias_kind":"arxiv_version","alias_value":"1104.0407v2","created_at":"2026-05-18T01:29:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1104.0407","created_at":"2026-05-18T01:29:22Z"},{"alias_kind":"pith_short_12","alias_value":"B2KBTUL3R356","created_at":"2026-05-18T12:26:24Z"},{"alias_kind":"pith_short_16","alias_value":"B2KBTUL3R356TRLZ","created_at":"2026-05-18T12:26:24Z"},{"alias_kind":"pith_short_8","alias_value":"B2KBTUL3","created_at":"2026-05-18T12:26:24Z"}],"graph_snapshots":[{"event_id":"sha256:0d589730ce96a1f40e57424b2daf69230acaa6751daff690dcbfed75bb310cc0","target":"graph","created_at":"2026-05-18T01:29:22Z","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":"A positive space is a space with a positive atlas, i.e. a collection of rational coordinate systems with subtraction free transition functions. The set of positive real points of a positive space is well defined. We define a tropical compactification of the latter. We show that it generalizes the Thurston compactification of a Teichmuller space. The tropical boundary of a positive space is a sphere with a piecewise linear structure. Cluster X-varieties are positive spaces of rather special type. We define special completions of cluster X-varieties. They have a stratification whose strata are (","authors_text":"A.B. Goncharov, V.V. Fock","cross_cats":["math.DG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-04-03T17:13:54Z","title":"Cluster X-varieties at infinity"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1104.0407","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:db3d8f2e549cb9172de3a2d34a2c1fb8003262f88a8c1480253b3132aecfa77c","target":"record","created_at":"2026-05-18T01:29:22Z","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":"a9c73791a9ac84206f374f7f5578a9a1ccd5347b02a093b0381440a059d14eaa","cross_cats_sorted":["math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-04-03T17:13:54Z","title_canon_sha256":"53c63f8d87ea7e3db74ceb985eeae6644d7427cb63d7136b313c9090ee043a35"},"schema_version":"1.0","source":{"id":"1104.0407","kind":"arxiv","version":2}},"canonical_sha256":"0e9419d17b8efbe9c57968f1794f9cd40c97171f366db253b7eac85f8fc786b1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0e9419d17b8efbe9c57968f1794f9cd40c97171f366db253b7eac85f8fc786b1","first_computed_at":"2026-05-18T01:29:22.269223Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:29:22.269223Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"8inPyDvkO+eviCK3vOvxVyo69adgyRBi0Jh4d8juiObnOTl9oyXUGPOie9G+k1UTMlmDixzLlcquDFYPT51TAw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:29:22.269886Z","signed_message":"canonical_sha256_bytes"},"source_id":"1104.0407","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:db3d8f2e549cb9172de3a2d34a2c1fb8003262f88a8c1480253b3132aecfa77c","sha256:0d589730ce96a1f40e57424b2daf69230acaa6751daff690dcbfed75bb310cc0"],"state_sha256":"6694268fb475c25b5f53338299d197200d2bd30325d26e6a7ca9094efb547e35"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"A5ngqyf3qxd4oy5FE3Ly+1FWnTJbCA0pgb1wHuumxs6VjLmgY9u+KbRdXgb7XQa9+xbCc4wIZvQeqYFtYB9nAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-25T22:53:37.891401Z","bundle_sha256":"388152811feffb8e0ab10f73b69da90e0869cbac22863117ac01e63dea01a64b"}}