{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:TJBPJ234Z6SJR2QCGZ4QWQQWOL","short_pith_number":"pith:TJBPJ234","canonical_record":{"source":{"id":"1809.08842","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2018-09-24T11:14:07Z","cross_cats_sorted":[],"title_canon_sha256":"5ac107f0eeaf3701baca09b2eea450fca3a34db014ef223375fc7b41e73aba53","abstract_canon_sha256":"4c395777296518c5d50417a6b57ac2a1816e08f869a4bf391893bb5d7b333ea3"},"schema_version":"1.0"},"canonical_sha256":"9a42f4eb7ccfa498ea0236790b421672f62888688451c603cbed2e52d4c3c6c8","source":{"kind":"arxiv","id":"1809.08842","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1809.08842","created_at":"2026-05-18T00:03:01Z"},{"alias_kind":"arxiv_version","alias_value":"1809.08842v1","created_at":"2026-05-18T00:03:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1809.08842","created_at":"2026-05-18T00:03:01Z"},{"alias_kind":"pith_short_12","alias_value":"TJBPJ234Z6SJ","created_at":"2026-05-18T12:32:53Z"},{"alias_kind":"pith_short_16","alias_value":"TJBPJ234Z6SJR2QC","created_at":"2026-05-18T12:32:53Z"},{"alias_kind":"pith_short_8","alias_value":"TJBPJ234","created_at":"2026-05-18T12:32:53Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:TJBPJ234Z6SJR2QCGZ4QWQQWOL","target":"record","payload":{"canonical_record":{"source":{"id":"1809.08842","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2018-09-24T11:14:07Z","cross_cats_sorted":[],"title_canon_sha256":"5ac107f0eeaf3701baca09b2eea450fca3a34db014ef223375fc7b41e73aba53","abstract_canon_sha256":"4c395777296518c5d50417a6b57ac2a1816e08f869a4bf391893bb5d7b333ea3"},"schema_version":"1.0"},"canonical_sha256":"9a42f4eb7ccfa498ea0236790b421672f62888688451c603cbed2e52d4c3c6c8","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:03:01.314089Z","signature_b64":"IpH/mz7PwrybT94+qSeyR5G8ZDDO8v1KKl0lWNH1uohBNTjgFSz02G92Z4lFIeQI7/z5dY3I+K0KI12VEJISCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9a42f4eb7ccfa498ea0236790b421672f62888688451c603cbed2e52d4c3c6c8","last_reissued_at":"2026-05-18T00:03:01.313357Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:03:01.313357Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1809.08842","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":"2026-05-18T00:03:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zEmNFZwZvxlI70yvpGHrWGM2AYz0PeTBj6+JCOuID9uX9H4MmQS/cHcft9rbq46cb6ldQm3uPsVEoSd+lOFrAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T23:08:19.056054Z"},"content_sha256":"3194d1456675192a311e3e179ae1064e1a6476973351539186c29b1489940c44","schema_version":"1.0","event_id":"sha256:3194d1456675192a311e3e179ae1064e1a6476973351539186c29b1489940c44"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:TJBPJ234Z6SJR2QCGZ4QWQQWOL","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Unusual scaling in a discrete quantum walk with random long range steps","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Parongama Sen","submitted_at":"2018-09-24T11:14:07Z","abstract_excerpt":"A discrete time quantum walker is considered in one dimension, where at each step, the translation can be more than one unit length chosen randomly. In the simplest case, the probability that the distance travelled is $\\ell$ is taken as $P(\\ell) = \\alpha \\delta(\\ell-1) + (1-\\alpha) \\delta (\\ell-2^n)$ with $n \\geq 1$. Even the $n=1$ case shows a drastic change in the scaling behaviour for any $\\alpha \\neq 0,1$. Specifically, $\\langle x^2\\rangle\n  \\propto t^{3/2}$ for $0 < \\alpha < 1$, implying the walk is slower compared to the usual quantum walk. This scaling behaviour, which is neither conven"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.08842","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":"2026-05-18T00:03:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jSnLMZc6CE3eeco5TbOLYcDcs2dlq+jItSA6ozh5SR1MCfRRZpHd9C8YOBD6vEMJV5QGtLsyt1uHxw3tVPtHAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T23:08:19.056453Z"},"content_sha256":"eef9b04457c85bf93de3a6650323a1411f8aff0175c99e8073bdfc36c7258622","schema_version":"1.0","event_id":"sha256:eef9b04457c85bf93de3a6650323a1411f8aff0175c99e8073bdfc36c7258622"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/TJBPJ234Z6SJR2QCGZ4QWQQWOL/bundle.json","state_url":"https://pith.science/pith/TJBPJ234Z6SJR2QCGZ4QWQQWOL/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/TJBPJ234Z6SJR2QCGZ4QWQQWOL/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":"2026-06-04T23:08:19Z","links":{"resolver":"https://pith.science/pith/TJBPJ234Z6SJR2QCGZ4QWQQWOL","bundle":"https://pith.science/pith/TJBPJ234Z6SJR2QCGZ4QWQQWOL/bundle.json","state":"https://pith.science/pith/TJBPJ234Z6SJR2QCGZ4QWQQWOL/state.json","well_known_bundle":"https://pith.science/.well-known/pith/TJBPJ234Z6SJR2QCGZ4QWQQWOL/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:TJBPJ234Z6SJR2QCGZ4QWQQWOL","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":"4c395777296518c5d50417a6b57ac2a1816e08f869a4bf391893bb5d7b333ea3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2018-09-24T11:14:07Z","title_canon_sha256":"5ac107f0eeaf3701baca09b2eea450fca3a34db014ef223375fc7b41e73aba53"},"schema_version":"1.0","source":{"id":"1809.08842","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1809.08842","created_at":"2026-05-18T00:03:01Z"},{"alias_kind":"arxiv_version","alias_value":"1809.08842v1","created_at":"2026-05-18T00:03:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1809.08842","created_at":"2026-05-18T00:03:01Z"},{"alias_kind":"pith_short_12","alias_value":"TJBPJ234Z6SJ","created_at":"2026-05-18T12:32:53Z"},{"alias_kind":"pith_short_16","alias_value":"TJBPJ234Z6SJR2QC","created_at":"2026-05-18T12:32:53Z"},{"alias_kind":"pith_short_8","alias_value":"TJBPJ234","created_at":"2026-05-18T12:32:53Z"}],"graph_snapshots":[{"event_id":"sha256:eef9b04457c85bf93de3a6650323a1411f8aff0175c99e8073bdfc36c7258622","target":"graph","created_at":"2026-05-18T00:03:01Z","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":"A discrete time quantum walker is considered in one dimension, where at each step, the translation can be more than one unit length chosen randomly. In the simplest case, the probability that the distance travelled is $\\ell$ is taken as $P(\\ell) = \\alpha \\delta(\\ell-1) + (1-\\alpha) \\delta (\\ell-2^n)$ with $n \\geq 1$. Even the $n=1$ case shows a drastic change in the scaling behaviour for any $\\alpha \\neq 0,1$. Specifically, $\\langle x^2\\rangle\n  \\propto t^{3/2}$ for $0 < \\alpha < 1$, implying the walk is slower compared to the usual quantum walk. This scaling behaviour, which is neither conven","authors_text":"Parongama Sen","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2018-09-24T11:14:07Z","title":"Unusual scaling in a discrete quantum walk with random long range steps"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.08842","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":"sha256:3194d1456675192a311e3e179ae1064e1a6476973351539186c29b1489940c44","target":"record","created_at":"2026-05-18T00:03:01Z","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":"4c395777296518c5d50417a6b57ac2a1816e08f869a4bf391893bb5d7b333ea3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2018-09-24T11:14:07Z","title_canon_sha256":"5ac107f0eeaf3701baca09b2eea450fca3a34db014ef223375fc7b41e73aba53"},"schema_version":"1.0","source":{"id":"1809.08842","kind":"arxiv","version":1}},"canonical_sha256":"9a42f4eb7ccfa498ea0236790b421672f62888688451c603cbed2e52d4c3c6c8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9a42f4eb7ccfa498ea0236790b421672f62888688451c603cbed2e52d4c3c6c8","first_computed_at":"2026-05-18T00:03:01.313357Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:03:01.313357Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"IpH/mz7PwrybT94+qSeyR5G8ZDDO8v1KKl0lWNH1uohBNTjgFSz02G92Z4lFIeQI7/z5dY3I+K0KI12VEJISCA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:03:01.314089Z","signed_message":"canonical_sha256_bytes"},"source_id":"1809.08842","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3194d1456675192a311e3e179ae1064e1a6476973351539186c29b1489940c44","sha256:eef9b04457c85bf93de3a6650323a1411f8aff0175c99e8073bdfc36c7258622"],"state_sha256":"98062dd4cf65eafe3f9b741b4f80cd7ce73f2321f5953c80f8fc1f61989d365f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8NjNkGsIKrR2Bk5YJi8VYWrqUojHTDrhYoLP6+WDKLecUqx7UX4HU7OPrSuhVA+AWBCMA+tdtzRoUJeLu/EbAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-04T23:08:19.058997Z","bundle_sha256":"ae5d35808d1136a8008812be72b70e8972e303846f60cdf47fd5e79aac9b4495"}}