{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:VBUULFYGPQT5ZJILWA3PHCWXKV","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":"5a90278b06d886d795d869ccab9a7bfcee18a171840f35060c8371060d4d0968","cross_cats_sorted":["math.MG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2017-05-23T17:39:57Z","title_canon_sha256":"c954f88068c25fa833cafcdea5a2b18e3946ff33eb30a481f1c61baf7f13efb7"},"schema_version":"1.0","source":{"id":"1705.08431","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1705.08431","created_at":"2026-05-17T23:53:12Z"},{"alias_kind":"arxiv_version","alias_value":"1705.08431v1","created_at":"2026-05-17T23:53:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.08431","created_at":"2026-05-17T23:53:12Z"},{"alias_kind":"pith_short_12","alias_value":"VBUULFYGPQT5","created_at":"2026-05-18T12:31:49Z"},{"alias_kind":"pith_short_16","alias_value":"VBUULFYGPQT5ZJIL","created_at":"2026-05-18T12:31:49Z"},{"alias_kind":"pith_short_8","alias_value":"VBUULFYG","created_at":"2026-05-18T12:31:49Z"}],"graph_snapshots":[{"event_id":"sha256:8a32200a62783a3c161302299f8da7d8a2b31c2ca72ac083238a737fd4bdeaec","target":"graph","created_at":"2026-05-17T23:53:12Z","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 provide an algebraic description of the Teichm\\\"uller space and moduli space of flat metrics on a closed manifold or orbifold and study its boundary, which consists of (isometry classes of) flat orbifolds to which the original object may collapse. It is also shown that every closed flat orbifold can be obtained by collapsing closed flat manifolds, and the collapsed limits of closed flat 3-manifolds are classified.","authors_text":"Andrzej Derdzinski, Paolo Piccione, Renato G. Bettiol","cross_cats":["math.MG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2017-05-23T17:39:57Z","title":"Teichm\\\"uller theory and collapse of flat manifolds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.08431","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":"sha256:0fa59f7810ecbe4278501b905165c730e6ddace2a46d74e5e5463ea677a6b68a","target":"record","created_at":"2026-05-17T23:53:12Z","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":"5a90278b06d886d795d869ccab9a7bfcee18a171840f35060c8371060d4d0968","cross_cats_sorted":["math.MG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2017-05-23T17:39:57Z","title_canon_sha256":"c954f88068c25fa833cafcdea5a2b18e3946ff33eb30a481f1c61baf7f13efb7"},"schema_version":"1.0","source":{"id":"1705.08431","kind":"arxiv","version":1}},"canonical_sha256":"a8694597067c27dca50bb036f38ad7556b34f27a0015b87b7dd259bfc493793f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a8694597067c27dca50bb036f38ad7556b34f27a0015b87b7dd259bfc493793f","first_computed_at":"2026-05-17T23:53:12.052213Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:53:12.052213Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"a3UuRh+dtGq7EdtvdCQ3dhumrNPgL/AEZSmPQdyVMEXcfoh0ihnwelxNa4EHelteLVGM3NXV8WlJYaoDqkcdDg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:53:12.052925Z","signed_message":"canonical_sha256_bytes"},"source_id":"1705.08431","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0fa59f7810ecbe4278501b905165c730e6ddace2a46d74e5e5463ea677a6b68a","sha256:8a32200a62783a3c161302299f8da7d8a2b31c2ca72ac083238a737fd4bdeaec"],"state_sha256":"3e821bea44255b7f6096b49fb78e00600153ed5904dd7b6f8c3eadc713c8f7dc"}