{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:HYIEW4SNTRGAHLIEB3FN7XPCSM","short_pith_number":"pith:HYIEW4SN","canonical_record":{"source":{"id":"1608.06208","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2016-08-10T13:50:17Z","cross_cats_sorted":["math.MG"],"title_canon_sha256":"d41c5d75c64d8e7c7fb30084de5f26c2121706e980ec88802880c2ac152aed81","abstract_canon_sha256":"e9aa3407f8b400eb9b168a058f107edf850e5b16dc65ef549532bcaa9b7f3213"},"schema_version":"1.0"},"canonical_sha256":"3e104b724d9c4c03ad040ecadfdde293293150b6ae53bed0e8f2635b9d0424c2","source":{"kind":"arxiv","id":"1608.06208","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1608.06208","created_at":"2026-05-18T00:57:43Z"},{"alias_kind":"arxiv_version","alias_value":"1608.06208v4","created_at":"2026-05-18T00:57:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1608.06208","created_at":"2026-05-18T00:57:43Z"},{"alias_kind":"pith_short_12","alias_value":"HYIEW4SNTRGA","created_at":"2026-05-18T12:30:22Z"},{"alias_kind":"pith_short_16","alias_value":"HYIEW4SNTRGAHLIE","created_at":"2026-05-18T12:30:22Z"},{"alias_kind":"pith_short_8","alias_value":"HYIEW4SN","created_at":"2026-05-18T12:30:22Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:HYIEW4SNTRGAHLIEB3FN7XPCSM","target":"record","payload":{"canonical_record":{"source":{"id":"1608.06208","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2016-08-10T13:50:17Z","cross_cats_sorted":["math.MG"],"title_canon_sha256":"d41c5d75c64d8e7c7fb30084de5f26c2121706e980ec88802880c2ac152aed81","abstract_canon_sha256":"e9aa3407f8b400eb9b168a058f107edf850e5b16dc65ef549532bcaa9b7f3213"},"schema_version":"1.0"},"canonical_sha256":"3e104b724d9c4c03ad040ecadfdde293293150b6ae53bed0e8f2635b9d0424c2","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:57:43.819093Z","signature_b64":"SrerGH7LxRQuLhzY7wc+c7K8JMWfzFLwdFXlRIvmzeIbcoLcJ/jq7bz5fJlYiopfPLMilab/pQs6upRbhHUVBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3e104b724d9c4c03ad040ecadfdde293293150b6ae53bed0e8f2635b9d0424c2","last_reissued_at":"2026-05-18T00:57:43.818513Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:57:43.818513Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1608.06208","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:57:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RSJlOSOeaTVmBmI9PxZeG+dO4fJOm2aoGkmsqgJcHfoQUQQKl9xA/b3ZAnoUINdg2NT8MJFSQ+uGa5W7bsJdCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-19T08:29:11.429124Z"},"content_sha256":"d9dd6d4f6db3d7c5a0cec28f8a0f1e2249ac82386db72ac8f1b19b76f187ed81","schema_version":"1.0","event_id":"sha256:d9dd6d4f6db3d7c5a0cec28f8a0f1e2249ac82386db72ac8f1b19b76f187ed81"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:HYIEW4SNTRGAHLIEB3FN7XPCSM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Two Forms of Proximal Physical Geometry. Axioms, Sewing Regions Together, Classes of Regions, Duality, and Parallel Fibre Bundles","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MG"],"primary_cat":"math.GN","authors_text":"J.F. Peters","submitted_at":"2016-08-10T13:50:17Z","abstract_excerpt":"This paper introduces two proximal forms of Lenzen physical geometry, namely, an \\emph{axiomatized strongly proximal physical geometry} that is built on simplicial complexes with the dualities and sewing operations derived from string geometry and an \\emph{axiomatized descriptive proximal physical geometry} in which spatial regions are described based on their features and the descriptive proximities between regions. This is a computational proximity approach to a Lenzen geometry of physical space. In both forms of physical geometry, region is a primitive. Intuitively, a region is a set of con"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.06208","kind":"arxiv","version":4},"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":"2026-05-18T00:57:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SX8kAUepEaZECbYNYIrvxOzzoYPxVUICRKXKwJrc8a8A3u8O6lLv5899erJMrBzZSZ7reUaJoPWVORnYde4PCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-19T08:29:11.429517Z"},"content_sha256":"cac9dba71f1c799ac539a04f66678d504c850422da8cbec7ab0b74cf41d5714d","schema_version":"1.0","event_id":"sha256:cac9dba71f1c799ac539a04f66678d504c850422da8cbec7ab0b74cf41d5714d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HYIEW4SNTRGAHLIEB3FN7XPCSM/bundle.json","state_url":"https://pith.science/pith/HYIEW4SNTRGAHLIEB3FN7XPCSM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HYIEW4SNTRGAHLIEB3FN7XPCSM/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":"2026-05-19T08:29:11Z","links":{"resolver":"https://pith.science/pith/HYIEW4SNTRGAHLIEB3FN7XPCSM","bundle":"https://pith.science/pith/HYIEW4SNTRGAHLIEB3FN7XPCSM/bundle.json","state":"https://pith.science/pith/HYIEW4SNTRGAHLIEB3FN7XPCSM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HYIEW4SNTRGAHLIEB3FN7XPCSM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:HYIEW4SNTRGAHLIEB3FN7XPCSM","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":"e9aa3407f8b400eb9b168a058f107edf850e5b16dc65ef549532bcaa9b7f3213","cross_cats_sorted":["math.MG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2016-08-10T13:50:17Z","title_canon_sha256":"d41c5d75c64d8e7c7fb30084de5f26c2121706e980ec88802880c2ac152aed81"},"schema_version":"1.0","source":{"id":"1608.06208","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1608.06208","created_at":"2026-05-18T00:57:43Z"},{"alias_kind":"arxiv_version","alias_value":"1608.06208v4","created_at":"2026-05-18T00:57:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1608.06208","created_at":"2026-05-18T00:57:43Z"},{"alias_kind":"pith_short_12","alias_value":"HYIEW4SNTRGA","created_at":"2026-05-18T12:30:22Z"},{"alias_kind":"pith_short_16","alias_value":"HYIEW4SNTRGAHLIE","created_at":"2026-05-18T12:30:22Z"},{"alias_kind":"pith_short_8","alias_value":"HYIEW4SN","created_at":"2026-05-18T12:30:22Z"}],"graph_snapshots":[{"event_id":"sha256:cac9dba71f1c799ac539a04f66678d504c850422da8cbec7ab0b74cf41d5714d","target":"graph","created_at":"2026-05-18T00:57:43Z","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":"This paper introduces two proximal forms of Lenzen physical geometry, namely, an \\emph{axiomatized strongly proximal physical geometry} that is built on simplicial complexes with the dualities and sewing operations derived from string geometry and an \\emph{axiomatized descriptive proximal physical geometry} in which spatial regions are described based on their features and the descriptive proximities between regions. This is a computational proximity approach to a Lenzen geometry of physical space. In both forms of physical geometry, region is a primitive. Intuitively, a region is a set of con","authors_text":"J.F. Peters","cross_cats":["math.MG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2016-08-10T13:50:17Z","title":"Two Forms of Proximal Physical Geometry. Axioms, Sewing Regions Together, Classes of Regions, Duality, and Parallel Fibre Bundles"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.06208","kind":"arxiv","version":4},"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:d9dd6d4f6db3d7c5a0cec28f8a0f1e2249ac82386db72ac8f1b19b76f187ed81","target":"record","created_at":"2026-05-18T00:57:43Z","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":"e9aa3407f8b400eb9b168a058f107edf850e5b16dc65ef549532bcaa9b7f3213","cross_cats_sorted":["math.MG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2016-08-10T13:50:17Z","title_canon_sha256":"d41c5d75c64d8e7c7fb30084de5f26c2121706e980ec88802880c2ac152aed81"},"schema_version":"1.0","source":{"id":"1608.06208","kind":"arxiv","version":4}},"canonical_sha256":"3e104b724d9c4c03ad040ecadfdde293293150b6ae53bed0e8f2635b9d0424c2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3e104b724d9c4c03ad040ecadfdde293293150b6ae53bed0e8f2635b9d0424c2","first_computed_at":"2026-05-18T00:57:43.818513Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:57:43.818513Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"SrerGH7LxRQuLhzY7wc+c7K8JMWfzFLwdFXlRIvmzeIbcoLcJ/jq7bz5fJlYiopfPLMilab/pQs6upRbhHUVBw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:57:43.819093Z","signed_message":"canonical_sha256_bytes"},"source_id":"1608.06208","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d9dd6d4f6db3d7c5a0cec28f8a0f1e2249ac82386db72ac8f1b19b76f187ed81","sha256:cac9dba71f1c799ac539a04f66678d504c850422da8cbec7ab0b74cf41d5714d"],"state_sha256":"5697ad7afb831b431d0aff7995d8e9a0b6749f4550102b923e53a58e03af5ead"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4pGSAtVTNgOKpyIBzU09qWPnTfqR9ods7i/PeqWerKwAkh5eVulfgbuUiEkIK1rAb50U/7djbGlLS3tlXxOeAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-19T08:29:11.431247Z","bundle_sha256":"cb26ceb3e9f652cf91489fce8178540f739e01bf4cf9d2183f961e2159b38dbc"}}