{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:LRMFWRMOJIBX32EEDREUQD7AK6","short_pith_number":"pith:LRMFWRMO","canonical_record":{"source":{"id":"1503.02184","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2015-03-07T15:03:13Z","cross_cats_sorted":["math.GT"],"title_canon_sha256":"4d2384e633b47249df8c12f09bc33fb6d13f621d5e3cb78b142ec89054ca7867","abstract_canon_sha256":"5016f07d41f1c7a8ac1476bcc735ce50d54ff25ebcbb4884c8a343cbaf902723"},"schema_version":"1.0"},"canonical_sha256":"5c585b458e4a037de8841c49480fe057b69e8fd271c731cf6f32e1f1be857902","source":{"kind":"arxiv","id":"1503.02184","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1503.02184","created_at":"2026-05-18T02:16:20Z"},{"alias_kind":"arxiv_version","alias_value":"1503.02184v2","created_at":"2026-05-18T02:16:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.02184","created_at":"2026-05-18T02:16:20Z"},{"alias_kind":"pith_short_12","alias_value":"LRMFWRMOJIBX","created_at":"2026-05-18T12:29:29Z"},{"alias_kind":"pith_short_16","alias_value":"LRMFWRMOJIBX32EE","created_at":"2026-05-18T12:29:29Z"},{"alias_kind":"pith_short_8","alias_value":"LRMFWRMO","created_at":"2026-05-18T12:29:29Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:LRMFWRMOJIBX32EEDREUQD7AK6","target":"record","payload":{"canonical_record":{"source":{"id":"1503.02184","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2015-03-07T15:03:13Z","cross_cats_sorted":["math.GT"],"title_canon_sha256":"4d2384e633b47249df8c12f09bc33fb6d13f621d5e3cb78b142ec89054ca7867","abstract_canon_sha256":"5016f07d41f1c7a8ac1476bcc735ce50d54ff25ebcbb4884c8a343cbaf902723"},"schema_version":"1.0"},"canonical_sha256":"5c585b458e4a037de8841c49480fe057b69e8fd271c731cf6f32e1f1be857902","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:16:20.107951Z","signature_b64":"0KwbRBRvBcXjrlTN4ZDCJPbtBEhKTo/99hFZnvjdjjIORGJ1n+NilDpYOAxCdXuJnM7umbEpfXGGgQxEymPcDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5c585b458e4a037de8841c49480fe057b69e8fd271c731cf6f32e1f1be857902","last_reissued_at":"2026-05-18T02:16:20.107335Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:16:20.107335Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1503.02184","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":"2026-05-18T02:16:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hyjVuJTqOwdnGwa4JrH8K44GBZOqoSxPZn3sj1hbKx3/v8fH3VbDPzQuALvsACPjo0ZDzvgoXd+nz4MYecCKBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T11:33:50.409076Z"},"content_sha256":"5204efdad703446ae08bc5139928e79dd74a64764d0e0582dc952822fd8f3882","schema_version":"1.0","event_id":"sha256:5204efdad703446ae08bc5139928e79dd74a64764d0e0582dc952822fd8f3882"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:LRMFWRMOJIBX32EEDREUQD7AK6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A pseudometric invariant under similarities in the hyperspace of non-degenerated compact convex sets of $\\mathbb R^n$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GT"],"primary_cat":"math.MG","authors_text":"Bernardo Gonz\\'alez Merino, Natalia Jonard-P\\'erez","submitted_at":"2015-03-07T15:03:13Z","abstract_excerpt":"In this work we define a new pseudometric in $\\mathcal K^n_*$, the hyperspace of all non-degenerated compact convex sets of $\\mathbb R^n$, which is invariant under similarities. We will prove that the quotient space generated by this pseudometric (which is the orbit space generated by the natural action of the group of similarities on $\\mathcal K^n_*$) is homeomorphic to the Banach-Mazur compactum $BM(n)$, while $\\mathcal K^n_*$ is homeomorphic to the topological product $Q\\times\\mathbb R^{n+1}$, where $Q$ stands for the Hilbert cube. Finally we will show some consequences in convex geometry, "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.02184","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":"2026-05-18T02:16:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wbiiffwTPV0rQItWx6RZEKTpVViBApEInmntZ3Tw6I0OEuAXKdzGeWCJ0OlrDbhJFNiBSMK8CpThOa1MdJVSAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T11:33:50.409442Z"},"content_sha256":"835650dfc4e0efcd1d7a17a125e34a1ecd9620bad2758180d33b2212dbfa9d04","schema_version":"1.0","event_id":"sha256:835650dfc4e0efcd1d7a17a125e34a1ecd9620bad2758180d33b2212dbfa9d04"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/LRMFWRMOJIBX32EEDREUQD7AK6/bundle.json","state_url":"https://pith.science/pith/LRMFWRMOJIBX32EEDREUQD7AK6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/LRMFWRMOJIBX32EEDREUQD7AK6/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":"2026-06-26T11:33:50Z","links":{"resolver":"https://pith.science/pith/LRMFWRMOJIBX32EEDREUQD7AK6","bundle":"https://pith.science/pith/LRMFWRMOJIBX32EEDREUQD7AK6/bundle.json","state":"https://pith.science/pith/LRMFWRMOJIBX32EEDREUQD7AK6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/LRMFWRMOJIBX32EEDREUQD7AK6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:LRMFWRMOJIBX32EEDREUQD7AK6","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":"5016f07d41f1c7a8ac1476bcc735ce50d54ff25ebcbb4884c8a343cbaf902723","cross_cats_sorted":["math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2015-03-07T15:03:13Z","title_canon_sha256":"4d2384e633b47249df8c12f09bc33fb6d13f621d5e3cb78b142ec89054ca7867"},"schema_version":"1.0","source":{"id":"1503.02184","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1503.02184","created_at":"2026-05-18T02:16:20Z"},{"alias_kind":"arxiv_version","alias_value":"1503.02184v2","created_at":"2026-05-18T02:16:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.02184","created_at":"2026-05-18T02:16:20Z"},{"alias_kind":"pith_short_12","alias_value":"LRMFWRMOJIBX","created_at":"2026-05-18T12:29:29Z"},{"alias_kind":"pith_short_16","alias_value":"LRMFWRMOJIBX32EE","created_at":"2026-05-18T12:29:29Z"},{"alias_kind":"pith_short_8","alias_value":"LRMFWRMO","created_at":"2026-05-18T12:29:29Z"}],"graph_snapshots":[{"event_id":"sha256:835650dfc4e0efcd1d7a17a125e34a1ecd9620bad2758180d33b2212dbfa9d04","target":"graph","created_at":"2026-05-18T02:16:20Z","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 work we define a new pseudometric in $\\mathcal K^n_*$, the hyperspace of all non-degenerated compact convex sets of $\\mathbb R^n$, which is invariant under similarities. We will prove that the quotient space generated by this pseudometric (which is the orbit space generated by the natural action of the group of similarities on $\\mathcal K^n_*$) is homeomorphic to the Banach-Mazur compactum $BM(n)$, while $\\mathcal K^n_*$ is homeomorphic to the topological product $Q\\times\\mathbb R^{n+1}$, where $Q$ stands for the Hilbert cube. Finally we will show some consequences in convex geometry, ","authors_text":"Bernardo Gonz\\'alez Merino, Natalia Jonard-P\\'erez","cross_cats":["math.GT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2015-03-07T15:03:13Z","title":"A pseudometric invariant under similarities in the hyperspace of non-degenerated compact convex sets of $\\mathbb R^n$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.02184","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":"sha256:5204efdad703446ae08bc5139928e79dd74a64764d0e0582dc952822fd8f3882","target":"record","created_at":"2026-05-18T02:16:20Z","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":"5016f07d41f1c7a8ac1476bcc735ce50d54ff25ebcbb4884c8a343cbaf902723","cross_cats_sorted":["math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2015-03-07T15:03:13Z","title_canon_sha256":"4d2384e633b47249df8c12f09bc33fb6d13f621d5e3cb78b142ec89054ca7867"},"schema_version":"1.0","source":{"id":"1503.02184","kind":"arxiv","version":2}},"canonical_sha256":"5c585b458e4a037de8841c49480fe057b69e8fd271c731cf6f32e1f1be857902","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5c585b458e4a037de8841c49480fe057b69e8fd271c731cf6f32e1f1be857902","first_computed_at":"2026-05-18T02:16:20.107335Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:16:20.107335Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"0KwbRBRvBcXjrlTN4ZDCJPbtBEhKTo/99hFZnvjdjjIORGJ1n+NilDpYOAxCdXuJnM7umbEpfXGGgQxEymPcDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:16:20.107951Z","signed_message":"canonical_sha256_bytes"},"source_id":"1503.02184","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5204efdad703446ae08bc5139928e79dd74a64764d0e0582dc952822fd8f3882","sha256:835650dfc4e0efcd1d7a17a125e34a1ecd9620bad2758180d33b2212dbfa9d04"],"state_sha256":"21eda4cf7ffb2a36779cf0b7258cb693dd4c55a39dfaeb0da309657e52198d7e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XjzhsUbrX5XDewkZJMXaUDB3PlrjC93XgSQCd65nXCfezTHRDqpuB4vx7GqnC7IW+R9Z5Pk43n2R7uk7uMWdCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-26T11:33:50.411402Z","bundle_sha256":"ef35dbcf3c918239589145e7c97b97eabbba4f9aad697be8b9e53e673ef24614"}}