{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2008:5MXBQ5MRFTJ6GXDQXEGWBQ3AMB","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":"4b42c27344301ab83bf64c64fbf3393a76a5e7ef39c39a785372df581626c241","cross_cats_sorted":["math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2008-04-01T10:58:47Z","title_canon_sha256":"35b67a056c69d4da8b84b678a4103aad0a9fae82758f30f09b793c6e322d2e77"},"schema_version":"1.0","source":{"id":"0804.0135","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0804.0135","created_at":"2026-05-17T23:53:56Z"},{"alias_kind":"arxiv_version","alias_value":"0804.0135v2","created_at":"2026-05-17T23:53:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0804.0135","created_at":"2026-05-17T23:53:56Z"},{"alias_kind":"pith_short_12","alias_value":"5MXBQ5MRFTJ6","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_16","alias_value":"5MXBQ5MRFTJ6GXDQ","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_8","alias_value":"5MXBQ5MR","created_at":"2026-05-18T12:25:56Z"}],"graph_snapshots":[{"event_id":"sha256:1affffda8d4d57a765c90ddf54f418b7cd8c4a649b811b926728a91d22556367","target":"graph","created_at":"2026-05-17T23:53:56Z","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 algebraic and geometric properties of metric spaces endowed with dilatation structures, which are emergent during the passage through smaller and smaller scales. In the limit we obtain a generalization of metric affine geometry, endowed with a noncommutative vector addition operation and with a modified version of ratio of three collinear points. This is the geometry of normed affine group spaces, a category which contains the ones of homogeneous groups, Carnot groups or contractible groups. In this category group operations are not fundamental, but derived objects, and the generaliza","authors_text":"Marius Buliga","cross_cats":["math.GR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2008-04-01T10:58:47Z","title":"Infinitesimal affine geometry of metric spaces endowed with a dilatation structure"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0804.0135","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":"sha256:14d9c1187125456d7306c992604b7111fce061d0ccf72bfb734eeef174677726","target":"record","created_at":"2026-05-17T23:53:56Z","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":"4b42c27344301ab83bf64c64fbf3393a76a5e7ef39c39a785372df581626c241","cross_cats_sorted":["math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2008-04-01T10:58:47Z","title_canon_sha256":"35b67a056c69d4da8b84b678a4103aad0a9fae82758f30f09b793c6e322d2e77"},"schema_version":"1.0","source":{"id":"0804.0135","kind":"arxiv","version":2}},"canonical_sha256":"eb2e1875912cd3e35c70b90d60c3606054c450dd90aef6fcdf567cf8c984aad9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"eb2e1875912cd3e35c70b90d60c3606054c450dd90aef6fcdf567cf8c984aad9","first_computed_at":"2026-05-17T23:53:56.003426Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:53:56.003426Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"v4qrzWyACJmlq3gBvJcvVPhgnXQIukCPS8nTIfaRA7f2aY0ea4b0SEYBpQhOr90Xemyb6wnQ7F8kTQaDLu+2CQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:53:56.003931Z","signed_message":"canonical_sha256_bytes"},"source_id":"0804.0135","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:14d9c1187125456d7306c992604b7111fce061d0ccf72bfb734eeef174677726","sha256:1affffda8d4d57a765c90ddf54f418b7cd8c4a649b811b926728a91d22556367"],"state_sha256":"b189049d91e62db2c787a141a33fb878351118895cb13fddb72e6ca8f384aae8"}