Pith Number

pith:67PHXXNN

pith:2000:67PHXXNNGXQLAPTXP2PFFASOID

not attested not anchored not stored refs pending

The elliptic curve in the S-duality theory and Eisenstein series for Kac-Moody groups

M. Kapranov

arxiv:math/0001005 v2 · 2000-01-02 · math.AG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{67PHXXNNGXQLAPTXP2PFFASOID}

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

Betti numbers of the moduli space of Higgs bundles over a real curve

Receipt and verification

First computed	2026-07-04T14:34:12.690805Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f7de7bddad35e0b03e777e9e52824e40c8e277cd7b34a879483d22c1efdf32a5

Aliases

arxiv: math/0001005 · arxiv_version: math/0001005v2 · doi: 10.48550/arxiv.math/0001005 · pith_short_12: 67PHXXNNGXQL · pith_short_16: 67PHXXNNGXQLAPTX · pith_short_8: 67PHXXNN

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/67PHXXNNGXQLAPTXP2PFFASOID \
  | 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: f7de7bddad35e0b03e777e9e52824e40c8e277cd7b34a879483d22c1efdf32a5

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9652c402ddb5ce00a09feb2c42eeaa7d214d752ff46cb6077ad9a97b3111625d",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "math.AG",
    "submitted_at": "2000-01-02T20:43:59Z",
    "title_canon_sha256": "f3a1d08eae89c99c7b5602f115f6526a640e12d82a93f8b0e613acb0d94a773b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0001005",
    "kind": "arxiv",
    "version": 2
  }
}