Pith Number

pith:MU73LZ7Y

pith:2001:MU73LZ7YY7KCP3SK2FMVBL3VHW

not attested not anchored not stored refs pending

Dirac's equation in 1+1 D from a random walk

M. Ibison

arxiv:quant-ph/0106105 v1 · 2001-06-19 · quant-ph

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{MU73LZ7YY7KCP3SK2FMVBL3VHW}

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	2026-07-04T14:45:39.414054Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

653fb5e7f8c7d427ee4ad15950af753d9a11a01f53100e97d081cadcf4ce0afd

Aliases

arxiv: quant-ph/0106105 · arxiv_version: quant-ph/0106105v1 · doi: 10.48550/arxiv.quant-ph/0106105 · pith_short_12: MU73LZ7YY7KC · pith_short_16: MU73LZ7YY7KCP3SK · pith_short_8: MU73LZ7Y

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/MU73LZ7YY7KCP3SK2FMVBL3VHW \
  | 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: 653fb5e7f8c7d427ee4ad15950af753d9a11a01f53100e97d081cadcf4ce0afd

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a9c52d3924b9076ded5bd5f5dac6281cbe973db5439d883c41a9b73e711f636d",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "quant-ph",
    "submitted_at": "2001-06-19T02:15:48Z",
    "title_canon_sha256": "2ed2cdc60b5c12e88f054c54f3beaaa4033c92c75059a6e58cdae6d1c3177411"
  },
  "schema_version": "1.0",
  "source": {
    "id": "quant-ph/0106105",
    "kind": "arxiv",
    "version": 1
  }
}