Pith Number

pith:T7GVZGDT

pith:2011:T7GVZGDTCOJK3BUKN4O7JHEXN6

not attested not anchored not stored refs pending

Asymptotic behavior of quantum walks on the line

Tatsuya Tate, Toshikazu Sunada

arxiv:1108.1878 v1 · 2011-08-09 · math.PR · math.FA

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{T7GVZGDTCOJK3BUKN4O7JHEXN6}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more · Embed verified badge

Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

✓ Portable graph bundle live · download bundle · merged state

The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Receipt and verification

First computed	2026-05-18T00:30:49.868575Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9fcd5c98731392ad868a6f1df49c976f826ea6106a08d63da534537b5e630be4

Aliases

arxiv: 1108.1878 · arxiv_version: 1108.1878v1 · doi: 10.48550/arxiv.1108.1878 · pith_short_12: T7GVZGDTCOJK · pith_short_16: T7GVZGDTCOJK3BUK · pith_short_8: T7GVZGDT

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/T7GVZGDTCOJK3BUKN4O7JHEXN6 \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: 9fcd5c98731392ad868a6f1df49c976f826ea6106a08d63da534537b5e630be4

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "132ff61d47e2edff7c29eae1ab28469b9767d26479331eecd5743ac351b56109",
    "cross_cats_sorted": [
      "math.FA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2011-08-09T08:31:34Z",
    "title_canon_sha256": "aff3a7b7a5283379511018837c5c215982d770183b21b7de248f03526b96976f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1108.1878",
    "kind": "arxiv",
    "version": 1
  }
}