{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:7RCSQWH2SPTBBO4LZMEMXZ4L5P","short_pith_number":"pith:7RCSQWH2","canonical_record":{"source":{"id":"1708.07429","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2017-08-24T14:08:28Z","cross_cats_sorted":[],"title_canon_sha256":"1cb81c51fae231686f10dbdde573decb01751a4f6a7772afd7d3e10284e815aa","abstract_canon_sha256":"520514d040a6abdec915f035a34412c360f80902902efe9dcb854cee24d951fa"},"schema_version":"1.0"},"canonical_sha256":"fc452858fa93e610bb8bcb08cbe78bebd144da3eaed5d0ac274b554c4d37f0c8","source":{"kind":"arxiv","id":"1708.07429","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1708.07429","created_at":"2026-05-18T00:36:44Z"},{"alias_kind":"arxiv_version","alias_value":"1708.07429v1","created_at":"2026-05-18T00:36:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1708.07429","created_at":"2026-05-18T00:36:44Z"},{"alias_kind":"pith_short_12","alias_value":"7RCSQWH2SPTB","created_at":"2026-05-18T12:31:05Z"},{"alias_kind":"pith_short_16","alias_value":"7RCSQWH2SPTBBO4L","created_at":"2026-05-18T12:31:05Z"},{"alias_kind":"pith_short_8","alias_value":"7RCSQWH2","created_at":"2026-05-18T12:31:05Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:7RCSQWH2SPTBBO4LZMEMXZ4L5P","target":"record","payload":{"canonical_record":{"source":{"id":"1708.07429","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2017-08-24T14:08:28Z","cross_cats_sorted":[],"title_canon_sha256":"1cb81c51fae231686f10dbdde573decb01751a4f6a7772afd7d3e10284e815aa","abstract_canon_sha256":"520514d040a6abdec915f035a34412c360f80902902efe9dcb854cee24d951fa"},"schema_version":"1.0"},"canonical_sha256":"fc452858fa93e610bb8bcb08cbe78bebd144da3eaed5d0ac274b554c4d37f0c8","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:36:44.349359Z","signature_b64":"01a9Ssbg6Ec1iaUnyFwPZCUXK9gnnOApbh3aZ2RvW+MaDGc1W0qL5ClTYLVDX+MDqgY/AH0uuIUtpBcGYrHLAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fc452858fa93e610bb8bcb08cbe78bebd144da3eaed5d0ac274b554c4d37f0c8","last_reissued_at":"2026-05-18T00:36:44.348884Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:36:44.348884Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1708.07429","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":"2026-05-18T00:36:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"woCruAg+M8Mij1+TA856kUkpc/iRiGFmZnzoJJoLcCREaEDX/yIW4Kx1mjIIBWi1Rw8QaHJ6xFGVX/P4NZlzBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-11T20:14:48.206632Z"},"content_sha256":"4d7cda99637da42c4aeb38c7acb19020a897f0b7d3b5713b95139a7ed9dd4daf","schema_version":"1.0","event_id":"sha256:4d7cda99637da42c4aeb38c7acb19020a897f0b7d3b5713b95139a7ed9dd4daf"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:7RCSQWH2SPTBBO4LZMEMXZ4L5P","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Quantum Pascal's Triangle and Sierpinski's carpet","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Harry Buhrman, Tom Bannink","submitted_at":"2017-08-24T14:08:28Z","abstract_excerpt":"In this paper we consider a quantum version of Pascal's triangle. Pascal's triangle is a well-known triangular array of numbers and when these numbers are plotted modulo 2, a fractal known as the Sierpinski triangle appears. We first prove the appearance of more general fractals when Pascal's triangle is considered modulo prime powers. The numbers in Pascal's triangle can be obtained by scaling the probabilities of the simple symmetric random walk on the line. In this paper we consider a quantum version of Pascal's triangle by replacing the random walk by the quantum walk known as the Hadamard"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.07429","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":"2026-05-18T00:36:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OzkyUuf/jYwnlCtAcYUi5Z9MQtwnyR8IQ7xq1tfwKtWo/A4mv/RHzxQ+HM5c150dGqOKFyeoAC/ZNcEl4MUEBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-11T20:14:48.207210Z"},"content_sha256":"009af34be31f8b842e59d3f69f1594af308cd034c39c7fe6b79825f5d29bc965","schema_version":"1.0","event_id":"sha256:009af34be31f8b842e59d3f69f1594af308cd034c39c7fe6b79825f5d29bc965"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7RCSQWH2SPTBBO4LZMEMXZ4L5P/bundle.json","state_url":"https://pith.science/pith/7RCSQWH2SPTBBO4LZMEMXZ4L5P/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7RCSQWH2SPTBBO4LZMEMXZ4L5P/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":"2026-08-11T20:14:48Z","links":{"resolver":"https://pith.science/pith/7RCSQWH2SPTBBO4LZMEMXZ4L5P","bundle":"https://pith.science/pith/7RCSQWH2SPTBBO4LZMEMXZ4L5P/bundle.json","state":"https://pith.science/pith/7RCSQWH2SPTBBO4LZMEMXZ4L5P/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7RCSQWH2SPTBBO4LZMEMXZ4L5P/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:7RCSQWH2SPTBBO4LZMEMXZ4L5P","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":"520514d040a6abdec915f035a34412c360f80902902efe9dcb854cee24d951fa","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2017-08-24T14:08:28Z","title_canon_sha256":"1cb81c51fae231686f10dbdde573decb01751a4f6a7772afd7d3e10284e815aa"},"schema_version":"1.0","source":{"id":"1708.07429","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1708.07429","created_at":"2026-05-18T00:36:44Z"},{"alias_kind":"arxiv_version","alias_value":"1708.07429v1","created_at":"2026-05-18T00:36:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1708.07429","created_at":"2026-05-18T00:36:44Z"},{"alias_kind":"pith_short_12","alias_value":"7RCSQWH2SPTB","created_at":"2026-05-18T12:31:05Z"},{"alias_kind":"pith_short_16","alias_value":"7RCSQWH2SPTBBO4L","created_at":"2026-05-18T12:31:05Z"},{"alias_kind":"pith_short_8","alias_value":"7RCSQWH2","created_at":"2026-05-18T12:31:05Z"}],"graph_snapshots":[{"event_id":"sha256:009af34be31f8b842e59d3f69f1594af308cd034c39c7fe6b79825f5d29bc965","target":"graph","created_at":"2026-05-18T00:36:44Z","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 paper we consider a quantum version of Pascal's triangle. Pascal's triangle is a well-known triangular array of numbers and when these numbers are plotted modulo 2, a fractal known as the Sierpinski triangle appears. We first prove the appearance of more general fractals when Pascal's triangle is considered modulo prime powers. The numbers in Pascal's triangle can be obtained by scaling the probabilities of the simple symmetric random walk on the line. In this paper we consider a quantum version of Pascal's triangle by replacing the random walk by the quantum walk known as the Hadamard","authors_text":"Harry Buhrman, Tom Bannink","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2017-08-24T14:08:28Z","title":"Quantum Pascal's Triangle and Sierpinski's carpet"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.07429","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":"sha256:4d7cda99637da42c4aeb38c7acb19020a897f0b7d3b5713b95139a7ed9dd4daf","target":"record","created_at":"2026-05-18T00:36:44Z","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":"520514d040a6abdec915f035a34412c360f80902902efe9dcb854cee24d951fa","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2017-08-24T14:08:28Z","title_canon_sha256":"1cb81c51fae231686f10dbdde573decb01751a4f6a7772afd7d3e10284e815aa"},"schema_version":"1.0","source":{"id":"1708.07429","kind":"arxiv","version":1}},"canonical_sha256":"fc452858fa93e610bb8bcb08cbe78bebd144da3eaed5d0ac274b554c4d37f0c8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fc452858fa93e610bb8bcb08cbe78bebd144da3eaed5d0ac274b554c4d37f0c8","first_computed_at":"2026-05-18T00:36:44.348884Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:36:44.348884Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"01a9Ssbg6Ec1iaUnyFwPZCUXK9gnnOApbh3aZ2RvW+MaDGc1W0qL5ClTYLVDX+MDqgY/AH0uuIUtpBcGYrHLAw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:36:44.349359Z","signed_message":"canonical_sha256_bytes"},"source_id":"1708.07429","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4d7cda99637da42c4aeb38c7acb19020a897f0b7d3b5713b95139a7ed9dd4daf","sha256:009af34be31f8b842e59d3f69f1594af308cd034c39c7fe6b79825f5d29bc965"],"state_sha256":"85bf2997fe82f647e52a7bf086b69a73e96f14d16b16d678664a62480876af0d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Zke/0x3KRNDfMx+3OJd2RDYVEZp+kEM1wiikUoqcljU0Oc1OteNewQKNU9uVfgSwmRDvn2jSslY1U5sf43q2Dg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-11T20:14:48.212332Z","bundle_sha256":"ea75a1267d71329e29d9f857ac8050ab95dc00c6d7db47db44cc7fe6401eba17"}}