Pith Number

pith:TUBA4XHL

pith:2008:TUBA4XHLEQMDHCQTONKE4BMR2U

not attested not anchored not stored refs pending

Modular differential equations and null vectors

Christoph A. Keller, Matthias R. Gaberdiel

arxiv:0804.0489 v3 · 2008-04-03 · 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{TUBA4XHLEQMDHCQTONKE4BMR2U}

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

Universal Modular Properties of Generalized Gibbs Ensembles and Chiral Deformations

Receipt and verification

First computed	2026-05-18T04:03:45.620545Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9d020e5ceb2418338a1373544e0591d50c9c44e3172a1837ff7d77f8ee2b37bd

Aliases

arxiv: 0804.0489 · arxiv_version: 0804.0489v3 · doi: 10.48550/arxiv.0804.0489 · pith_short_12: TUBA4XHLEQMD · pith_short_16: TUBA4XHLEQMDHCQT · pith_short_8: TUBA4XHL

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/TUBA4XHLEQMDHCQTONKE4BMR2U \
  | 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: 9d020e5ceb2418338a1373544e0591d50c9c44e3172a1837ff7d77f8ee2b37bd

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "20940b80c34a026ef2d4db7b860266e238cb769d5eeb6e0a4b053f68bc2efef2",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "hep-th",
    "submitted_at": "2008-04-03T07:49:10Z",
    "title_canon_sha256": "93cad8f4ba2c7cb1c2bbfea1165993d0c734cf0e3c9010e21171220a5789aa16"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0804.0489",
    "kind": "arxiv",
    "version": 3
  }
}