{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:H3JTI3PW3DJ4VEZMVIHD3WZGYJ","short_pith_number":"pith:H3JTI3PW","canonical_record":{"source":{"id":"1712.04130","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-12-12T04:57:55Z","cross_cats_sorted":["cs.CR"],"title_canon_sha256":"ad7132fcaf200b81609acede6e58855d7074358869f6890f9d1310024b660295","abstract_canon_sha256":"78b62ab703bbfcba4b90efff54f8e3a3dac2fcb1c96637e06bd4bab288496d43"},"schema_version":"1.0"},"canonical_sha256":"3ed3346df6d8d3ca932caa0e3ddb26c26d8c864edeaedd9b7ae22a4a5520d0e8","source":{"kind":"arxiv","id":"1712.04130","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1712.04130","created_at":"2026-05-18T00:28:09Z"},{"alias_kind":"arxiv_version","alias_value":"1712.04130v1","created_at":"2026-05-18T00:28:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1712.04130","created_at":"2026-05-18T00:28:09Z"},{"alias_kind":"pith_short_12","alias_value":"H3JTI3PW3DJ4","created_at":"2026-05-18T12:31:18Z"},{"alias_kind":"pith_short_16","alias_value":"H3JTI3PW3DJ4VEZM","created_at":"2026-05-18T12:31:18Z"},{"alias_kind":"pith_short_8","alias_value":"H3JTI3PW","created_at":"2026-05-18T12:31:18Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:H3JTI3PW3DJ4VEZMVIHD3WZGYJ","target":"record","payload":{"canonical_record":{"source":{"id":"1712.04130","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-12-12T04:57:55Z","cross_cats_sorted":["cs.CR"],"title_canon_sha256":"ad7132fcaf200b81609acede6e58855d7074358869f6890f9d1310024b660295","abstract_canon_sha256":"78b62ab703bbfcba4b90efff54f8e3a3dac2fcb1c96637e06bd4bab288496d43"},"schema_version":"1.0"},"canonical_sha256":"3ed3346df6d8d3ca932caa0e3ddb26c26d8c864edeaedd9b7ae22a4a5520d0e8","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:28:09.060147Z","signature_b64":"eWy75REJCE5qPDZmrO9ZFkqbON6wH7SSPyXE+eFzsXx4kdbFavd1zvmNeQ8IO3/F/Y0JdXdiKqnGlJHSimVbDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3ed3346df6d8d3ca932caa0e3ddb26c26d8c864edeaedd9b7ae22a4a5520d0e8","last_reissued_at":"2026-05-18T00:28:09.059595Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:28:09.059595Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1712.04130","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":"2026-05-18T00:28:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wob2TzLHF0HwDMEpsvogmnfehuGg3Y4w9m7IIbge0S82t82apnpdEufu03OlZYe/aM58bYrsBt/WeEXdo5rXCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T14:39:21.534328Z"},"content_sha256":"4eb52ebf1f90adcf290a0d9adabbf8a0df320332cd7168a8aba4f5c1e0c6db5c","schema_version":"1.0","event_id":"sha256:4eb52ebf1f90adcf290a0d9adabbf8a0df320332cd7168a8aba4f5c1e0c6db5c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:H3JTI3PW3DJ4VEZMVIHD3WZGYJ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Topology of Privacy: Lattice Structures and Information Bubbles for Inference and Obfuscation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CR"],"primary_cat":"math.CO","authors_text":"Michael Erdmann","submitted_at":"2017-12-12T04:57:55Z","abstract_excerpt":"Information has intrinsic geometric and topological structure, arising from relative relationships beyond absolute values or types. For instance, the fact that two people share a meal describes a relationship independent of the meal's ingredients. Multiple such relationships give rise to relations and their lattices. Lattices have topology. That topology informs the ways in which information may be observed, hidden, inferred, and dissembled.\n  Dowker's Theorem establishes a homotopy equivalence between two simplicial complexes derived from a relation. From a privacy perspective, one complex de"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.04130","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":""},"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":"2026-05-18T00:28:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"glH6CpYXkNqnzBgdGId1bwrT4Gvsu1pu9A8yEOLr1kxxg460RGsvHalIqGHbmb1XxpWP3I2zLx/du7CJz1bfCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T14:39:21.534681Z"},"content_sha256":"dd7a3ce8d8a93711550cc5a6639a822ed0588819f0f48d450f5e78339365d7fe","schema_version":"1.0","event_id":"sha256:dd7a3ce8d8a93711550cc5a6639a822ed0588819f0f48d450f5e78339365d7fe"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/H3JTI3PW3DJ4VEZMVIHD3WZGYJ/bundle.json","state_url":"https://pith.science/pith/H3JTI3PW3DJ4VEZMVIHD3WZGYJ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/H3JTI3PW3DJ4VEZMVIHD3WZGYJ/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":"2026-06-10T14:39:21Z","links":{"resolver":"https://pith.science/pith/H3JTI3PW3DJ4VEZMVIHD3WZGYJ","bundle":"https://pith.science/pith/H3JTI3PW3DJ4VEZMVIHD3WZGYJ/bundle.json","state":"https://pith.science/pith/H3JTI3PW3DJ4VEZMVIHD3WZGYJ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/H3JTI3PW3DJ4VEZMVIHD3WZGYJ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:H3JTI3PW3DJ4VEZMVIHD3WZGYJ","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":"78b62ab703bbfcba4b90efff54f8e3a3dac2fcb1c96637e06bd4bab288496d43","cross_cats_sorted":["cs.CR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-12-12T04:57:55Z","title_canon_sha256":"ad7132fcaf200b81609acede6e58855d7074358869f6890f9d1310024b660295"},"schema_version":"1.0","source":{"id":"1712.04130","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1712.04130","created_at":"2026-05-18T00:28:09Z"},{"alias_kind":"arxiv_version","alias_value":"1712.04130v1","created_at":"2026-05-18T00:28:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1712.04130","created_at":"2026-05-18T00:28:09Z"},{"alias_kind":"pith_short_12","alias_value":"H3JTI3PW3DJ4","created_at":"2026-05-18T12:31:18Z"},{"alias_kind":"pith_short_16","alias_value":"H3JTI3PW3DJ4VEZM","created_at":"2026-05-18T12:31:18Z"},{"alias_kind":"pith_short_8","alias_value":"H3JTI3PW","created_at":"2026-05-18T12:31:18Z"}],"graph_snapshots":[{"event_id":"sha256:dd7a3ce8d8a93711550cc5a6639a822ed0588819f0f48d450f5e78339365d7fe","target":"graph","created_at":"2026-05-18T00:28:09Z","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":"Information has intrinsic geometric and topological structure, arising from relative relationships beyond absolute values or types. For instance, the fact that two people share a meal describes a relationship independent of the meal's ingredients. Multiple such relationships give rise to relations and their lattices. Lattices have topology. That topology informs the ways in which information may be observed, hidden, inferred, and dissembled.\n  Dowker's Theorem establishes a homotopy equivalence between two simplicial complexes derived from a relation. From a privacy perspective, one complex de","authors_text":"Michael Erdmann","cross_cats":["cs.CR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-12-12T04:57:55Z","title":"Topology of Privacy: Lattice Structures and Information Bubbles for Inference and Obfuscation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.04130","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":"sha256:4eb52ebf1f90adcf290a0d9adabbf8a0df320332cd7168a8aba4f5c1e0c6db5c","target":"record","created_at":"2026-05-18T00:28:09Z","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":"78b62ab703bbfcba4b90efff54f8e3a3dac2fcb1c96637e06bd4bab288496d43","cross_cats_sorted":["cs.CR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-12-12T04:57:55Z","title_canon_sha256":"ad7132fcaf200b81609acede6e58855d7074358869f6890f9d1310024b660295"},"schema_version":"1.0","source":{"id":"1712.04130","kind":"arxiv","version":1}},"canonical_sha256":"3ed3346df6d8d3ca932caa0e3ddb26c26d8c864edeaedd9b7ae22a4a5520d0e8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3ed3346df6d8d3ca932caa0e3ddb26c26d8c864edeaedd9b7ae22a4a5520d0e8","first_computed_at":"2026-05-18T00:28:09.059595Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:28:09.059595Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"eWy75REJCE5qPDZmrO9ZFkqbON6wH7SSPyXE+eFzsXx4kdbFavd1zvmNeQ8IO3/F/Y0JdXdiKqnGlJHSimVbDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:28:09.060147Z","signed_message":"canonical_sha256_bytes"},"source_id":"1712.04130","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4eb52ebf1f90adcf290a0d9adabbf8a0df320332cd7168a8aba4f5c1e0c6db5c","sha256:dd7a3ce8d8a93711550cc5a6639a822ed0588819f0f48d450f5e78339365d7fe"],"state_sha256":"9d540de81a13df3c2a6c03075443c7cb2bfd748383164f458883cb044d79edb5"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fLRKOjfCjPcrTgCyoMv1AsEB69WpVXMAYJajJQWGTxpkDWYYk0I0eB0QDLXxfmC8glauilSOjBkjww54F/ucCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-10T14:39:21.536722Z","bundle_sha256":"76cd54eb10e402a59cc216adb574ee99ffe0e989ed4aaddea1acd8a3d1f4a0bd"}}