Pith Number

pith:VYGZ5G7K

pith:2013:VYGZ5G7K33QPLOIJRBTXTFCRX3

not attested not anchored not stored refs pending

Fourier expansions of Kac-Moody Eisenstein series and degenerate Whittaker vectors

Axel Kleinschmidt, Daniel Persson, Philipp Fleig

arxiv:1312.3643 v2 · 2013-12-12 · hep-th · math.NT · math.RT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{VYGZ5G7K33QPLOIJRBTXTFCRX3}

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	2026-05-18T02:25:49.236631Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ae0d9e9beadee0f5b9098867799451beec05765276c78a32c6655ef7a7afdfd5

Aliases

arxiv: 1312.3643 · arxiv_version: 1312.3643v2 · doi: 10.48550/arxiv.1312.3643 · pith_short_12: VYGZ5G7K33QP · pith_short_16: VYGZ5G7K33QPLOIJ · pith_short_8: VYGZ5G7K

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/VYGZ5G7K33QPLOIJRBTXTFCRX3 \
  | 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: ae0d9e9beadee0f5b9098867799451beec05765276c78a32c6655ef7a7afdfd5

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "49bf134f9d4551207a6293971a04716cb72e53b394a0fb0223c87f6333ed9cf0",
    "cross_cats_sorted": [
      "math.NT",
      "math.RT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "hep-th",
    "submitted_at": "2013-12-12T21:00:32Z",
    "title_canon_sha256": "39c80b7df4336a87e293eab7bb3b5397eb7c77b8a6b8b2815ef2ad73f141dc2f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1312.3643",
    "kind": "arxiv",
    "version": 2
  }
}