Pith Number

pith:U5U62EE7

pith:2016:U5U62EE7KW65E65DXEIQUTALJN

not attested not anchored not stored refs pending

Three-loop vacuum integrals with arbitrary masses

Ayres Freitas

arxiv:1609.09159 v3 · 2016-09-29 · hep-ph · hep-th

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\usepackage{pith}
\pithnumber{U5U62EE7KW65E65DXEIQUTALJN}

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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

TVID 2: Evaluation of planar-type three-loop self-energy integrals with arbitrary masses

Receipt and verification

First computed	2026-07-05T02:29:51.334501Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a769ed109f55bdd27ba3b9110a4c0b4b57ae2b9f5dedf837d5dcd2fac979db89

Aliases

arxiv: 1609.09159 · arxiv_version: 1609.09159v3 · doi: 10.48550/arxiv.1609.09159 · pith_short_12: U5U62EE7KW65 · pith_short_16: U5U62EE7KW65E65D · pith_short_8: U5U62EE7

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/U5U62EE7KW65E65DXEIQUTALJN \
  | 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: a769ed109f55bdd27ba3b9110a4c0b4b57ae2b9f5dedf837d5dcd2fac979db89

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c209feff228a35d95f4fe7ff673df26c4cf8700087d64fe41285a0cf4af094a9",
    "cross_cats_sorted": [
      "hep-th"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "hep-ph",
    "submitted_at": "2016-09-29T00:10:23Z",
    "title_canon_sha256": "2a3378ef46fc871437ff0d8b09f5f3b2a412d9f85cfb9576ab0f48e89e093283"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1609.09159",
    "kind": "arxiv",
    "version": 3
  }
}