{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:W7YU7THLTGDT4GAUFQMIBIPKIP","short_pith_number":"pith:W7YU7THL","canonical_record":{"source":{"id":"2407.03295","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2024-07-03T17:29:17Z","cross_cats_sorted":[],"title_canon_sha256":"7b52edeb7ac7ca870f32dfca492c8cd61464d0e2f8e984d3d8d6f86e0c03bddf","abstract_canon_sha256":"2dff693b91abb613d4abccb37086fd6625e59cc24e1c373c5e21056578630d6c"},"schema_version":"1.0"},"canonical_sha256":"b7f14fcceb99873e18142c1880a1ea43ee2fb97db8d8c04085100f973bc759da","source":{"kind":"arxiv","id":"2407.03295","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2407.03295","created_at":"2026-07-05T08:39:48Z"},{"alias_kind":"arxiv_version","alias_value":"2407.03295v1","created_at":"2026-07-05T08:39:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2407.03295","created_at":"2026-07-05T08:39:48Z"},{"alias_kind":"pith_short_12","alias_value":"W7YU7THLTGDT","created_at":"2026-07-05T08:39:48Z"},{"alias_kind":"pith_short_16","alias_value":"W7YU7THLTGDT4GAU","created_at":"2026-07-05T08:39:48Z"},{"alias_kind":"pith_short_8","alias_value":"W7YU7THL","created_at":"2026-07-05T08:39:48Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:W7YU7THLTGDT4GAUFQMIBIPKIP","target":"record","payload":{"canonical_record":{"source":{"id":"2407.03295","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2024-07-03T17:29:17Z","cross_cats_sorted":[],"title_canon_sha256":"7b52edeb7ac7ca870f32dfca492c8cd61464d0e2f8e984d3d8d6f86e0c03bddf","abstract_canon_sha256":"2dff693b91abb613d4abccb37086fd6625e59cc24e1c373c5e21056578630d6c"},"schema_version":"1.0"},"canonical_sha256":"b7f14fcceb99873e18142c1880a1ea43ee2fb97db8d8c04085100f973bc759da","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T08:39:48.707150Z","signature_b64":"5jrTFSUTNK/vW+ancHnicgtV95DACDR7OqSZsAHY6yQJ6OSTpJjNYyodMpo4l82/ih8NDZnt1LHSpzzyQgKPAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b7f14fcceb99873e18142c1880a1ea43ee2fb97db8d8c04085100f973bc759da","last_reissued_at":"2026-07-05T08:39:48.706668Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T08:39:48.706668Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2407.03295","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T08:39:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yLh8OHVd8eAO7Dh5mHnpZ4LmZEVqYRYGmnmcJbFdEifGyup81DyJPegyJr98+yTVUI0ur4rv4OuklBnddGS5Cg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-21T16:49:47.714041Z"},"content_sha256":"e6099dc94dbfc9c3848dd8a8c01d1c04544a500e57af5eb236a742ef3ab10346","schema_version":"1.0","event_id":"sha256:e6099dc94dbfc9c3848dd8a8c01d1c04544a500e57af5eb236a742ef3ab10346"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:W7YU7THLTGDT4GAUFQMIBIPKIP","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Embedding-Projection Correspondences for the estimation of the Gromov-Hausdorff distance","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.MG","authors_text":"Facundo M\\'emoli, Zane T. Smith","submitted_at":"2024-07-03T17:29:17Z","abstract_excerpt":"This writeup describes ongoing work on designing and testing a certain family of correspondences between compact metric spaces that we call \\emph{embedding-projection correspondences} (EPCs). Of particular interest are EPCs between spheres of different dimension."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2407.03295","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2407.03295/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T08:39:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"iD2sucNHEfPWqWKSEC3spaqxcTXJWP43N1ExamFM/TXdRhjL1EgjwwwJEihIj0rcS3QrXuBhnepgEvsh3cYGBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-21T16:49:47.714563Z"},"content_sha256":"24401d67c125e206265459bb96fe4aa488aa7336fb777fc27a6dfdc1e2405049","schema_version":"1.0","event_id":"sha256:24401d67c125e206265459bb96fe4aa488aa7336fb777fc27a6dfdc1e2405049"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/W7YU7THLTGDT4GAUFQMIBIPKIP/bundle.json","state_url":"https://pith.science/pith/W7YU7THLTGDT4GAUFQMIBIPKIP/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/W7YU7THLTGDT4GAUFQMIBIPKIP/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":"2026-08-21T16:49:47Z","links":{"resolver":"https://pith.science/pith/W7YU7THLTGDT4GAUFQMIBIPKIP","bundle":"https://pith.science/pith/W7YU7THLTGDT4GAUFQMIBIPKIP/bundle.json","state":"https://pith.science/pith/W7YU7THLTGDT4GAUFQMIBIPKIP/state.json","well_known_bundle":"https://pith.science/.well-known/pith/W7YU7THLTGDT4GAUFQMIBIPKIP/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:W7YU7THLTGDT4GAUFQMIBIPKIP","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":"2dff693b91abb613d4abccb37086fd6625e59cc24e1c373c5e21056578630d6c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2024-07-03T17:29:17Z","title_canon_sha256":"7b52edeb7ac7ca870f32dfca492c8cd61464d0e2f8e984d3d8d6f86e0c03bddf"},"schema_version":"1.0","source":{"id":"2407.03295","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2407.03295","created_at":"2026-07-05T08:39:48Z"},{"alias_kind":"arxiv_version","alias_value":"2407.03295v1","created_at":"2026-07-05T08:39:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2407.03295","created_at":"2026-07-05T08:39:48Z"},{"alias_kind":"pith_short_12","alias_value":"W7YU7THLTGDT","created_at":"2026-07-05T08:39:48Z"},{"alias_kind":"pith_short_16","alias_value":"W7YU7THLTGDT4GAU","created_at":"2026-07-05T08:39:48Z"},{"alias_kind":"pith_short_8","alias_value":"W7YU7THL","created_at":"2026-07-05T08:39:48Z"}],"graph_snapshots":[{"event_id":"sha256:24401d67c125e206265459bb96fe4aa488aa7336fb777fc27a6dfdc1e2405049","target":"graph","created_at":"2026-07-05T08:39:48Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2407.03295/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"This writeup describes ongoing work on designing and testing a certain family of correspondences between compact metric spaces that we call \\emph{embedding-projection correspondences} (EPCs). Of particular interest are EPCs between spheres of different dimension.","authors_text":"Facundo M\\'emoli, Zane T. Smith","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2024-07-03T17:29:17Z","title":"Embedding-Projection Correspondences for the estimation of the Gromov-Hausdorff distance"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2407.03295","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:e6099dc94dbfc9c3848dd8a8c01d1c04544a500e57af5eb236a742ef3ab10346","target":"record","created_at":"2026-07-05T08:39:48Z","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":"2dff693b91abb613d4abccb37086fd6625e59cc24e1c373c5e21056578630d6c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2024-07-03T17:29:17Z","title_canon_sha256":"7b52edeb7ac7ca870f32dfca492c8cd61464d0e2f8e984d3d8d6f86e0c03bddf"},"schema_version":"1.0","source":{"id":"2407.03295","kind":"arxiv","version":1}},"canonical_sha256":"b7f14fcceb99873e18142c1880a1ea43ee2fb97db8d8c04085100f973bc759da","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b7f14fcceb99873e18142c1880a1ea43ee2fb97db8d8c04085100f973bc759da","first_computed_at":"2026-07-05T08:39:48.706668Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T08:39:48.706668Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"5jrTFSUTNK/vW+ancHnicgtV95DACDR7OqSZsAHY6yQJ6OSTpJjNYyodMpo4l82/ih8NDZnt1LHSpzzyQgKPAg==","signature_status":"signed_v1","signed_at":"2026-07-05T08:39:48.707150Z","signed_message":"canonical_sha256_bytes"},"source_id":"2407.03295","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e6099dc94dbfc9c3848dd8a8c01d1c04544a500e57af5eb236a742ef3ab10346","sha256:24401d67c125e206265459bb96fe4aa488aa7336fb777fc27a6dfdc1e2405049"],"state_sha256":"a398d5e02172af0556068abcf9d5cef9a7bb36a9769985285bdcae49bfc2f834"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pkS/2DjlyDp5O6Q8wKsV8599NC9COKS2/MSx9wZ7VbXHp/oL+Mlmi6G1hSLANM7TdelU7TdzUzNKfO+24MjnCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-21T16:49:47.718748Z","bundle_sha256":"57bd93af3da7188f9ad6054a3f96f3918e1402356016aa43a98a78527cc2e0e0"}}