Pith Number

pith:AZZEDJP3

pith:2015:AZZEDJP3LO2WJI7F43RQ2ANSZN

not attested not anchored not stored refs pending

Hopf algebra and renormalization: A brief review

Usman Naseer

arxiv:1505.04765 v1 · 2015-05-18 · math-ph · math.MP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{AZZEDJP3LO2WJI7F43RQ2ANSZN}

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

Homomorphism, substructure, and ideal: Elementary but rigorous aspects of renormalization group or hierarchical structure of topological orders

Receipt and verification

First computed	2026-05-18T02:07:24.661156Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

067241a5fb5bb564a3e5e6e30d01b2cb6b322c96831b922b89e21d477dbbcb3b

Aliases

arxiv: 1505.04765 · arxiv_version: 1505.04765v1 · doi: 10.48550/arxiv.1505.04765 · pith_short_12: AZZEDJP3LO2W · pith_short_16: AZZEDJP3LO2WJI7F · pith_short_8: AZZEDJP3

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/AZZEDJP3LO2WJI7F43RQ2ANSZN \
  | 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: 067241a5fb5bb564a3e5e6e30d01b2cb6b322c96831b922b89e21d477dbbcb3b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f7bb83c61c69c6b3021f5775ae8d969fde2c94d0b8a259c7df82e0ff66d11606",
    "cross_cats_sorted": [
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2015-05-18T19:12:48Z",
    "title_canon_sha256": "b7cd1b2d1820bf780d67538388843edb35b982d91233b2b66c052f96f1fc116f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1505.04765",
    "kind": "arxiv",
    "version": 1
  }
}