{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:A66QJ6VBKXZ5R5LT4O4G253VZ5","short_pith_number":"pith:A66QJ6VB","canonical_record":{"source":{"id":"1506.03754","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-06-11T17:40:34Z","cross_cats_sorted":[],"title_canon_sha256":"2295f20d0558a161ec10fd22e22d2d6d862eb55b977e97f839129f0edd909d6f","abstract_canon_sha256":"7321a2e9203ff2577aba779c0eca1dcfe7087f11c1feca4df3bf9d420a8a3998"},"schema_version":"1.0"},"canonical_sha256":"07bd04faa155f3d8f573e3b86d7775cf49006a62d58ae4fde229c30887c1d442","source":{"kind":"arxiv","id":"1506.03754","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1506.03754","created_at":"2026-05-18T00:41:48Z"},{"alias_kind":"arxiv_version","alias_value":"1506.03754v3","created_at":"2026-05-18T00:41:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1506.03754","created_at":"2026-05-18T00:41:48Z"},{"alias_kind":"pith_short_12","alias_value":"A66QJ6VBKXZ5","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_16","alias_value":"A66QJ6VBKXZ5R5LT","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_8","alias_value":"A66QJ6VB","created_at":"2026-05-18T12:29:10Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:A66QJ6VBKXZ5R5LT4O4G253VZ5","target":"record","payload":{"canonical_record":{"source":{"id":"1506.03754","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-06-11T17:40:34Z","cross_cats_sorted":[],"title_canon_sha256":"2295f20d0558a161ec10fd22e22d2d6d862eb55b977e97f839129f0edd909d6f","abstract_canon_sha256":"7321a2e9203ff2577aba779c0eca1dcfe7087f11c1feca4df3bf9d420a8a3998"},"schema_version":"1.0"},"canonical_sha256":"07bd04faa155f3d8f573e3b86d7775cf49006a62d58ae4fde229c30887c1d442","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:41:48.084629Z","signature_b64":"igl4Bm/4Exi7ca6E9mJOX5HeD42HV6nXdgngFTjHc6Ev57MfJCQCkJij0VmrngfvHFX0I7Owfb8KDc0OEfxuAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"07bd04faa155f3d8f573e3b86d7775cf49006a62d58ae4fde229c30887c1d442","last_reissued_at":"2026-05-18T00:41:48.084040Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:41:48.084040Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1506.03754","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":"2026-05-18T00:41:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ko8aGbSziEAdSMHUFSncbSsgty66cBtwb2UqTvItuP9DG0cRBQA2WLhC8uz03pVXwZe+O9jikSOAlgjp6kByDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T09:54:35.497976Z"},"content_sha256":"6189c588c8c85c1ffc6a7ce4ef881c69cc5dfc0ea8dac7f210c7d7717b677657","schema_version":"1.0","event_id":"sha256:6189c588c8c85c1ffc6a7ce4ef881c69cc5dfc0ea8dac7f210c7d7717b677657"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:A66QJ6VBKXZ5R5LT4O4G253VZ5","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Skeletons of stable maps I: Rational curves in toric varieties","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Dhruv Ranganathan","submitted_at":"2015-06-11T17:40:34Z","abstract_excerpt":"We study the Berkovich analytification of the space of genus $0$ logarithmic stable maps to a toric variety $X$ and present applications to both algebraic and tropical geometry. On algebraic side, insights from tropical geometry give two new geometric descriptions of this space of maps -- (1) as an explicit toroidal modification of $\\overline M_{0,n}\\times X$ and (2) as a tropical compactification in a toric variety. On the combinatorial side, we prove that the tropicalization of the space of genus $0$ logarithmic stable maps coincides with the space of tropical stable maps, giving a large new"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.03754","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":"2026-05-18T00:41:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"F5+LUx0Cf4X81SDMHAWu+SDEN4PheV6bGQ+IZMkLJrhrlTkU8rjmdDnL0+rEndzzcKuK+vZt+cZ3+vzMoRREAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T09:54:35.498664Z"},"content_sha256":"018fa0a5007e4ffe286b714b0ad8f4fe7734017757c5a1bc62c694730c517c4c","schema_version":"1.0","event_id":"sha256:018fa0a5007e4ffe286b714b0ad8f4fe7734017757c5a1bc62c694730c517c4c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/A66QJ6VBKXZ5R5LT4O4G253VZ5/bundle.json","state_url":"https://pith.science/pith/A66QJ6VBKXZ5R5LT4O4G253VZ5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/A66QJ6VBKXZ5R5LT4O4G253VZ5/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":"2026-05-30T09:54:35Z","links":{"resolver":"https://pith.science/pith/A66QJ6VBKXZ5R5LT4O4G253VZ5","bundle":"https://pith.science/pith/A66QJ6VBKXZ5R5LT4O4G253VZ5/bundle.json","state":"https://pith.science/pith/A66QJ6VBKXZ5R5LT4O4G253VZ5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/A66QJ6VBKXZ5R5LT4O4G253VZ5/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:A66QJ6VBKXZ5R5LT4O4G253VZ5","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":"7321a2e9203ff2577aba779c0eca1dcfe7087f11c1feca4df3bf9d420a8a3998","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-06-11T17:40:34Z","title_canon_sha256":"2295f20d0558a161ec10fd22e22d2d6d862eb55b977e97f839129f0edd909d6f"},"schema_version":"1.0","source":{"id":"1506.03754","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1506.03754","created_at":"2026-05-18T00:41:48Z"},{"alias_kind":"arxiv_version","alias_value":"1506.03754v3","created_at":"2026-05-18T00:41:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1506.03754","created_at":"2026-05-18T00:41:48Z"},{"alias_kind":"pith_short_12","alias_value":"A66QJ6VBKXZ5","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_16","alias_value":"A66QJ6VBKXZ5R5LT","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_8","alias_value":"A66QJ6VB","created_at":"2026-05-18T12:29:10Z"}],"graph_snapshots":[{"event_id":"sha256:018fa0a5007e4ffe286b714b0ad8f4fe7734017757c5a1bc62c694730c517c4c","target":"graph","created_at":"2026-05-18T00:41:48Z","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":"We study the Berkovich analytification of the space of genus $0$ logarithmic stable maps to a toric variety $X$ and present applications to both algebraic and tropical geometry. On algebraic side, insights from tropical geometry give two new geometric descriptions of this space of maps -- (1) as an explicit toroidal modification of $\\overline M_{0,n}\\times X$ and (2) as a tropical compactification in a toric variety. On the combinatorial side, we prove that the tropicalization of the space of genus $0$ logarithmic stable maps coincides with the space of tropical stable maps, giving a large new","authors_text":"Dhruv Ranganathan","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-06-11T17:40:34Z","title":"Skeletons of stable maps I: Rational curves in toric varieties"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.03754","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":"sha256:6189c588c8c85c1ffc6a7ce4ef881c69cc5dfc0ea8dac7f210c7d7717b677657","target":"record","created_at":"2026-05-18T00:41:48Z","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":"7321a2e9203ff2577aba779c0eca1dcfe7087f11c1feca4df3bf9d420a8a3998","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-06-11T17:40:34Z","title_canon_sha256":"2295f20d0558a161ec10fd22e22d2d6d862eb55b977e97f839129f0edd909d6f"},"schema_version":"1.0","source":{"id":"1506.03754","kind":"arxiv","version":3}},"canonical_sha256":"07bd04faa155f3d8f573e3b86d7775cf49006a62d58ae4fde229c30887c1d442","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"07bd04faa155f3d8f573e3b86d7775cf49006a62d58ae4fde229c30887c1d442","first_computed_at":"2026-05-18T00:41:48.084040Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:41:48.084040Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"igl4Bm/4Exi7ca6E9mJOX5HeD42HV6nXdgngFTjHc6Ev57MfJCQCkJij0VmrngfvHFX0I7Owfb8KDc0OEfxuAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:41:48.084629Z","signed_message":"canonical_sha256_bytes"},"source_id":"1506.03754","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6189c588c8c85c1ffc6a7ce4ef881c69cc5dfc0ea8dac7f210c7d7717b677657","sha256:018fa0a5007e4ffe286b714b0ad8f4fe7734017757c5a1bc62c694730c517c4c"],"state_sha256":"e15b8fe38514492bb5a569ad50bf4146d1c8f175a80f0b706846016065deb737"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Q3DSRlGhparF/LkJw6aTZ/RFjwZElGxz6gojo3d5qXvFOMoiQ5oBivc3I7aMuUwIa1As3tGF0TpQtsHb+eYQCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T09:54:35.503311Z","bundle_sha256":"004d705e5120c139e2aef864f4f79a2d53d6291f5266903f3537db53e10d772f"}}