{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:QR5OLIMNVOS77PDOZH5XRMRQ2O","short_pith_number":"pith:QR5OLIMN","canonical_record":{"source":{"id":"1204.3875","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2012-04-17T18:42:29Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"e65ec56dc7e0cf8f1b653b462dbb5331cfac64bc8f9829e59a43b15e3723df9d","abstract_canon_sha256":"38ab256e749ecf10994d3597a705c04ba89cc1197b3214d903564c648a84c0cd"},"schema_version":"1.0"},"canonical_sha256":"847ae5a18daba5ffbc6ec9fb78b230d3ad864d9f3bfbbabd0091eda67f8767e0","source":{"kind":"arxiv","id":"1204.3875","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1204.3875","created_at":"2026-05-18T03:03:44Z"},{"alias_kind":"arxiv_version","alias_value":"1204.3875v2","created_at":"2026-05-18T03:03:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1204.3875","created_at":"2026-05-18T03:03:44Z"},{"alias_kind":"pith_short_12","alias_value":"QR5OLIMNVOS7","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_16","alias_value":"QR5OLIMNVOS77PDO","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_8","alias_value":"QR5OLIMN","created_at":"2026-05-18T12:27:18Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:QR5OLIMNVOS77PDOZH5XRMRQ2O","target":"record","payload":{"canonical_record":{"source":{"id":"1204.3875","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2012-04-17T18:42:29Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"e65ec56dc7e0cf8f1b653b462dbb5331cfac64bc8f9829e59a43b15e3723df9d","abstract_canon_sha256":"38ab256e749ecf10994d3597a705c04ba89cc1197b3214d903564c648a84c0cd"},"schema_version":"1.0"},"canonical_sha256":"847ae5a18daba5ffbc6ec9fb78b230d3ad864d9f3bfbbabd0091eda67f8767e0","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:03:44.868833Z","signature_b64":"GVYeyat5rzymZW3jZgAdo/bebUeUnQ08Rk2cYVLG4l7zCYTyNxPfw22yIkyJjWDE+7cRbumxuJ7bbdRDOwgsBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"847ae5a18daba5ffbc6ec9fb78b230d3ad864d9f3bfbbabd0091eda67f8767e0","last_reissued_at":"2026-05-18T03:03:44.868251Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:03:44.868251Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1204.3875","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":"2026-05-18T03:03:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yJJwhR6M/4mZK2bNNiw7rkvjxHOfMA5d7KIxO06f+5fIu2XSpo80w1imBtdowXlN/QwXknop5y81fR0VqTcKBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T11:18:08.734468Z"},"content_sha256":"27867affa2f4aa6994679ac3e16446b417ef1c3acd1116128bfca081a20dd45a","schema_version":"1.0","event_id":"sha256:27867affa2f4aa6994679ac3e16446b417ef1c3acd1116128bfca081a20dd45a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:QR5OLIMNVOS77PDOZH5XRMRQ2O","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Tropicalizing vs Compactifying the Torelli morphism","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.AG","authors_text":"Filippo Viviani","submitted_at":"2012-04-17T18:42:29Z","abstract_excerpt":"In this paper, we compare the compactified Torelli morphism (as defined by V. Alexeev) and the tropical Torelli map (as defined by the author in a joint work with S. Brannetti and M. Melo, and furthered studied by M. Chan). Our aim is twofold: on one hand, we will review the construction and main properties of the above mentioned two Torelli maps, focusing in particular on the description of their fibers achieved by the author in joint works with L. Caporaso; on the other hand, we will clarify the relationship between the two Torelli maps via the introduction of the reduction maps and the trop"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.3875","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":"2026-05-18T03:03:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"oDA2dKRzqlgWsW3q9Rd/0jLDwjENvDenmGk8F6ccn7kCJst9Y2294byHpmQLj8WWJ5FpILU3FqbqPp3Kw0JyDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T11:18:08.734805Z"},"content_sha256":"cccbd5eeb25aee937031f47410186e17e78d583b77d3c89e43fd61a7c28fcf88","schema_version":"1.0","event_id":"sha256:cccbd5eeb25aee937031f47410186e17e78d583b77d3c89e43fd61a7c28fcf88"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QR5OLIMNVOS77PDOZH5XRMRQ2O/bundle.json","state_url":"https://pith.science/pith/QR5OLIMNVOS77PDOZH5XRMRQ2O/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QR5OLIMNVOS77PDOZH5XRMRQ2O/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":"2026-06-22T11:18:08Z","links":{"resolver":"https://pith.science/pith/QR5OLIMNVOS77PDOZH5XRMRQ2O","bundle":"https://pith.science/pith/QR5OLIMNVOS77PDOZH5XRMRQ2O/bundle.json","state":"https://pith.science/pith/QR5OLIMNVOS77PDOZH5XRMRQ2O/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QR5OLIMNVOS77PDOZH5XRMRQ2O/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:QR5OLIMNVOS77PDOZH5XRMRQ2O","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":"38ab256e749ecf10994d3597a705c04ba89cc1197b3214d903564c648a84c0cd","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2012-04-17T18:42:29Z","title_canon_sha256":"e65ec56dc7e0cf8f1b653b462dbb5331cfac64bc8f9829e59a43b15e3723df9d"},"schema_version":"1.0","source":{"id":"1204.3875","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1204.3875","created_at":"2026-05-18T03:03:44Z"},{"alias_kind":"arxiv_version","alias_value":"1204.3875v2","created_at":"2026-05-18T03:03:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1204.3875","created_at":"2026-05-18T03:03:44Z"},{"alias_kind":"pith_short_12","alias_value":"QR5OLIMNVOS7","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_16","alias_value":"QR5OLIMNVOS77PDO","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_8","alias_value":"QR5OLIMN","created_at":"2026-05-18T12:27:18Z"}],"graph_snapshots":[{"event_id":"sha256:cccbd5eeb25aee937031f47410186e17e78d583b77d3c89e43fd61a7c28fcf88","target":"graph","created_at":"2026-05-18T03:03:44Z","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 compare the compactified Torelli morphism (as defined by V. Alexeev) and the tropical Torelli map (as defined by the author in a joint work with S. Brannetti and M. Melo, and furthered studied by M. Chan). Our aim is twofold: on one hand, we will review the construction and main properties of the above mentioned two Torelli maps, focusing in particular on the description of their fibers achieved by the author in joint works with L. Caporaso; on the other hand, we will clarify the relationship between the two Torelli maps via the introduction of the reduction maps and the trop","authors_text":"Filippo Viviani","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2012-04-17T18:42:29Z","title":"Tropicalizing vs Compactifying the Torelli morphism"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.3875","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":"sha256:27867affa2f4aa6994679ac3e16446b417ef1c3acd1116128bfca081a20dd45a","target":"record","created_at":"2026-05-18T03:03:44Z","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":"38ab256e749ecf10994d3597a705c04ba89cc1197b3214d903564c648a84c0cd","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2012-04-17T18:42:29Z","title_canon_sha256":"e65ec56dc7e0cf8f1b653b462dbb5331cfac64bc8f9829e59a43b15e3723df9d"},"schema_version":"1.0","source":{"id":"1204.3875","kind":"arxiv","version":2}},"canonical_sha256":"847ae5a18daba5ffbc6ec9fb78b230d3ad864d9f3bfbbabd0091eda67f8767e0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"847ae5a18daba5ffbc6ec9fb78b230d3ad864d9f3bfbbabd0091eda67f8767e0","first_computed_at":"2026-05-18T03:03:44.868251Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:03:44.868251Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"GVYeyat5rzymZW3jZgAdo/bebUeUnQ08Rk2cYVLG4l7zCYTyNxPfw22yIkyJjWDE+7cRbumxuJ7bbdRDOwgsBA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:03:44.868833Z","signed_message":"canonical_sha256_bytes"},"source_id":"1204.3875","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:27867affa2f4aa6994679ac3e16446b417ef1c3acd1116128bfca081a20dd45a","sha256:cccbd5eeb25aee937031f47410186e17e78d583b77d3c89e43fd61a7c28fcf88"],"state_sha256":"93d21f62323a8629970320f7ad09913ae0052735d147665bd4739d9b92db8ea6"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8V41kjMQQ7lOxalxqHL0tf09NJyQ8mqrZwunaMpcYCoSWM1z3Zo3CcWcv1vCa/i3TUIBQkYzT32R/52o/qUpCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-22T11:18:08.736653Z","bundle_sha256":"4b7bc3ea2abd272d79043dff623eabef4b80e7aeff94b20e4cb865791bba2e70"}}