Pith Number

pith:H3FFRJLK

pith:2021:H3FFRJLKOMZZSAFM2XO7ZV6NPD

not attested not anchored not stored refs pending

Loop-tree duality from vertices and edges

William J. Torres Bobadilla

arxiv:2102.05048 v3 · 2021-02-09 · hep-ph · hep-th

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{H3FFRJLKOMZZSAFM2XO7ZV6NPD}

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.

Cited by

1 paper in Pith

General finite two-loop amplitude integrand for photoproduction in quark annihilation

Receipt and verification

First computed	2026-07-05T02:51:17.248387Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3eca58a56a73339900acd5ddfcd7cd78f68875f924f70c2a07f9be7f1346cb52

Aliases

arxiv: 2102.05048 · arxiv_version: 2102.05048v3 · doi: 10.48550/arxiv.2102.05048 · pith_short_12: H3FFRJLKOMZZ · pith_short_16: H3FFRJLKOMZZSAFM · pith_short_8: H3FFRJLK

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/H3FFRJLKOMZZSAFM2XO7ZV6NPD \
  | 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: 3eca58a56a73339900acd5ddfcd7cd78f68875f924f70c2a07f9be7f1346cb52

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d181b75a47430492c152a479432577df06276e406e1866c2dbd2d4b564f30dfd",
    "cross_cats_sorted": [
      "hep-th"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "hep-ph",
    "submitted_at": "2021-02-09T19:00:00Z",
    "title_canon_sha256": "e0c3c77a3344a27484022bbf5bb41b07e34790cb4bfae15eaff289f10355e4fd"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2102.05048",
    "kind": "arxiv",
    "version": 3
  }
}