{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:EFT45QYTUTEWSH7G2NDX6H7FYL","short_pith_number":"pith:EFT45QYT","canonical_record":{"source":{"id":"1110.1917","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-10-10T03:38:23Z","cross_cats_sorted":["math.MP","quant-ph"],"title_canon_sha256":"5df39d38bce018464ed0e0236e6368909130f94aa30a574b51737093dc8b7bac","abstract_canon_sha256":"2b5260ebc5faf0964cce9f9a6a60bea00ee04b48e4c20bbbdfec8e2c99f67b81"},"schema_version":"1.0"},"canonical_sha256":"2167cec313a4c9691fe6d3477f1fe5c2d3d1e68f8b86ae547d8fa6befa97475f","source":{"kind":"arxiv","id":"1110.1917","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1110.1917","created_at":"2026-05-18T04:11:19Z"},{"alias_kind":"arxiv_version","alias_value":"1110.1917v1","created_at":"2026-05-18T04:11:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1110.1917","created_at":"2026-05-18T04:11:19Z"},{"alias_kind":"pith_short_12","alias_value":"EFT45QYTUTEW","created_at":"2026-05-18T12:26:28Z"},{"alias_kind":"pith_short_16","alias_value":"EFT45QYTUTEWSH7G","created_at":"2026-05-18T12:26:28Z"},{"alias_kind":"pith_short_8","alias_value":"EFT45QYT","created_at":"2026-05-18T12:26:28Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:EFT45QYTUTEWSH7G2NDX6H7FYL","target":"record","payload":{"canonical_record":{"source":{"id":"1110.1917","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-10-10T03:38:23Z","cross_cats_sorted":["math.MP","quant-ph"],"title_canon_sha256":"5df39d38bce018464ed0e0236e6368909130f94aa30a574b51737093dc8b7bac","abstract_canon_sha256":"2b5260ebc5faf0964cce9f9a6a60bea00ee04b48e4c20bbbdfec8e2c99f67b81"},"schema_version":"1.0"},"canonical_sha256":"2167cec313a4c9691fe6d3477f1fe5c2d3d1e68f8b86ae547d8fa6befa97475f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:11:19.320198Z","signature_b64":"TjkDJVPV8SUV2QiBqCWzlCWqRn4QeQxQnV/5G54TFQ7wmqZoGr58UdqmSN0mdydkj9acglW66tu65hZUhtaHCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2167cec313a4c9691fe6d3477f1fe5c2d3d1e68f8b86ae547d8fa6befa97475f","last_reissued_at":"2026-05-18T04:11:19.319735Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:11:19.319735Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1110.1917","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":"2026-05-18T04:11:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GtEEB588mFVLa4PTIIi6syYEReYkD9dyaTq3xtH47mNTlMzGV4b56Bd59frCJ0MX5gJ1b8XYG819ZVRcHKNSDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T19:56:42.725101Z"},"content_sha256":"521090b3ee9969c577c60bddcfa94f1aa950bcf061aa1616e6c318bf625830fe","schema_version":"1.0","event_id":"sha256:521090b3ee9969c577c60bddcfa94f1aa950bcf061aa1616e6c318bf625830fe"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:EFT45QYTUTEWSH7G2NDX6H7FYL","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Von Neumann Entanglement and Decoherence in Two Dimensional Quantum Walks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP","quant-ph"],"primary_cat":"math-ph","authors_text":"Clement Ampadu","submitted_at":"2011-10-10T03:38:23Z","abstract_excerpt":"Using the concept of von Neumann entropy, we quantify the information content of the various components of the quantum walk system, including the mutual information between its subsystems (coin and position) and use it to give a precise formulation of the measure of entanglement between subsystems."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.1917","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":"2026-05-18T04:11:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"eWKe+kjIte1+B7y/T5DdIcV1kUckKUkVQVP238Q1LHgUjBySahrRUASAPx+NkRA+xo9MUQsw2nQ5Nv9Vv6cVDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T19:56:42.725587Z"},"content_sha256":"2088c6f9c6dbbaf255a2b899a0700b0dbfcdcb9c6c5683fe50edecfcdf01c121","schema_version":"1.0","event_id":"sha256:2088c6f9c6dbbaf255a2b899a0700b0dbfcdcb9c6c5683fe50edecfcdf01c121"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/EFT45QYTUTEWSH7G2NDX6H7FYL/bundle.json","state_url":"https://pith.science/pith/EFT45QYTUTEWSH7G2NDX6H7FYL/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/EFT45QYTUTEWSH7G2NDX6H7FYL/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":"2026-06-06T19:56:42Z","links":{"resolver":"https://pith.science/pith/EFT45QYTUTEWSH7G2NDX6H7FYL","bundle":"https://pith.science/pith/EFT45QYTUTEWSH7G2NDX6H7FYL/bundle.json","state":"https://pith.science/pith/EFT45QYTUTEWSH7G2NDX6H7FYL/state.json","well_known_bundle":"https://pith.science/.well-known/pith/EFT45QYTUTEWSH7G2NDX6H7FYL/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:EFT45QYTUTEWSH7G2NDX6H7FYL","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":"2b5260ebc5faf0964cce9f9a6a60bea00ee04b48e4c20bbbdfec8e2c99f67b81","cross_cats_sorted":["math.MP","quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-10-10T03:38:23Z","title_canon_sha256":"5df39d38bce018464ed0e0236e6368909130f94aa30a574b51737093dc8b7bac"},"schema_version":"1.0","source":{"id":"1110.1917","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1110.1917","created_at":"2026-05-18T04:11:19Z"},{"alias_kind":"arxiv_version","alias_value":"1110.1917v1","created_at":"2026-05-18T04:11:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1110.1917","created_at":"2026-05-18T04:11:19Z"},{"alias_kind":"pith_short_12","alias_value":"EFT45QYTUTEW","created_at":"2026-05-18T12:26:28Z"},{"alias_kind":"pith_short_16","alias_value":"EFT45QYTUTEWSH7G","created_at":"2026-05-18T12:26:28Z"},{"alias_kind":"pith_short_8","alias_value":"EFT45QYT","created_at":"2026-05-18T12:26:28Z"}],"graph_snapshots":[{"event_id":"sha256:2088c6f9c6dbbaf255a2b899a0700b0dbfcdcb9c6c5683fe50edecfcdf01c121","target":"graph","created_at":"2026-05-18T04:11:19Z","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":"Using the concept of von Neumann entropy, we quantify the information content of the various components of the quantum walk system, including the mutual information between its subsystems (coin and position) and use it to give a precise formulation of the measure of entanglement between subsystems.","authors_text":"Clement Ampadu","cross_cats":["math.MP","quant-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-10-10T03:38:23Z","title":"Von Neumann Entanglement and Decoherence in Two Dimensional Quantum Walks"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.1917","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":"sha256:521090b3ee9969c577c60bddcfa94f1aa950bcf061aa1616e6c318bf625830fe","target":"record","created_at":"2026-05-18T04:11:19Z","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":"2b5260ebc5faf0964cce9f9a6a60bea00ee04b48e4c20bbbdfec8e2c99f67b81","cross_cats_sorted":["math.MP","quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-10-10T03:38:23Z","title_canon_sha256":"5df39d38bce018464ed0e0236e6368909130f94aa30a574b51737093dc8b7bac"},"schema_version":"1.0","source":{"id":"1110.1917","kind":"arxiv","version":1}},"canonical_sha256":"2167cec313a4c9691fe6d3477f1fe5c2d3d1e68f8b86ae547d8fa6befa97475f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2167cec313a4c9691fe6d3477f1fe5c2d3d1e68f8b86ae547d8fa6befa97475f","first_computed_at":"2026-05-18T04:11:19.319735Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:11:19.319735Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"TjkDJVPV8SUV2QiBqCWzlCWqRn4QeQxQnV/5G54TFQ7wmqZoGr58UdqmSN0mdydkj9acglW66tu65hZUhtaHCg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:11:19.320198Z","signed_message":"canonical_sha256_bytes"},"source_id":"1110.1917","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:521090b3ee9969c577c60bddcfa94f1aa950bcf061aa1616e6c318bf625830fe","sha256:2088c6f9c6dbbaf255a2b899a0700b0dbfcdcb9c6c5683fe50edecfcdf01c121"],"state_sha256":"e197db2df7871530e914050baf84eef6a3879526d156ae702ef1360232f6bb51"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"78vx9xYpQUZAS5uxzWTvLbJbWgR/YvJKz1SJCTVSjTrbJrL9I9KvONfOaxgzYPH59h9KjOa8TtdYL6vBYw4zCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-06T19:56:42.728616Z","bundle_sha256":"fca966979e853d14581266a930216271e400372c591f141a69d1da73a5f3000f"}}