Pith Number

pith:ILBQYFQS

pith:2014:ILBQYFQSEW3BOMW3AFLLTLA265

not attested not anchored not stored refs pending

A "strange" functional equation for Eisenstein series and miraculous duality on the moduli stack of bundles

D. Gaitsgory

arxiv:1404.6780 v3 · 2014-04-27 · 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{ILBQYFQSEW3BOMW3AFLLTLA265}

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	2026-05-18T01:15:24.109829Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

42c30c161225b61732db0156b9ac1af7577ec313d649f1d599cfb3d2883f752c

Aliases

arxiv: 1404.6780 · arxiv_version: 1404.6780v3 · doi: 10.48550/arxiv.1404.6780 · pith_short_12: ILBQYFQSEW3B · pith_short_16: ILBQYFQSEW3BOMW3 · pith_short_8: ILBQYFQS

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/ILBQYFQSEW3BOMW3AFLLTLA265 \
  | 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: 42c30c161225b61732db0156b9ac1af7577ec313d649f1d599cfb3d2883f752c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7d2caa8fe3d5b1c02e57e0a9e2c58df1264755a945a19895b1c552da9bf62506",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2014-04-27T16:08:37Z",
    "title_canon_sha256": "3a3cf2caf6a41cab93e147cd1219421f82db1d629a9aa066ecf206618d0bdcfa"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1404.6780",
    "kind": "arxiv",
    "version": 3
  }
}