Pith Number

pith:3EDE3BFZ

pith:2007:3EDE3BFZY27LAYCVAHLDZYLBPL

not attested not anchored not stored refs pending

Recursion Relations for One-Loop Gravity Amplitudes

Andreas Brandhuber, Bill Spence, Gabriele Travaglini, Simon McNamara

arxiv:hep-th/0701187 v2 · 2007-01-19 · 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{3EDE3BFZY27LAYCVAHLDZYLBPL}

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	2026-05-18T04:38:25.123631Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d9064d84b9c6beb0605501d63ce1617af38ea9bfd8df3d66998cf15e6caec0b8

Aliases

arxiv: hep-th/0701187 · arxiv_version: hep-th/0701187v2 · doi: 10.48550/arxiv.hep-th/0701187 · pith_short_12: 3EDE3BFZY27L · pith_short_16: 3EDE3BFZY27LAYCV · pith_short_8: 3EDE3BFZ

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/3EDE3BFZY27LAYCVAHLDZYLBPL \
  | 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: d9064d84b9c6beb0605501d63ce1617af38ea9bfd8df3d66998cf15e6caec0b8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "dbc099b306e1a5a1081a6d4b850ccd7083a986652c4e9f237c7faec050bffce9",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "hep-th",
    "submitted_at": "2007-01-19T18:47:29Z",
    "title_canon_sha256": "9037ff0159f87f7ee075d9095dd5b52201f8ac02fbeacabc76a87950bdc9a99a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "hep-th/0701187",
    "kind": "arxiv",
    "version": 2
  }
}