Pith Number

pith:3S6I65KN

pith:2015:3S6I65KNALSXAH7M2VWYSDXPZW

not attested not anchored not stored refs pending

Explicit construction of Ramanujan bigraphs

Amy Wooding, Brooke Feigon, Cristina Ballantine, Janne Kool, Kathrin Maurischat, Radhika Ganapathy

arxiv:1502.02739 v1 · 2015-02-09 · math.NT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{3S6I65KNALSXAH7M2VWYSDXPZW}

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	2026-05-18T02:27:31.078536Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

dcbc8f754d02e5701fecd56d890eefcd812cc37efcfbc222fe589fa66a505713

Aliases

arxiv: 1502.02739 · arxiv_version: 1502.02739v1 · doi: 10.48550/arxiv.1502.02739 · pith_short_12: 3S6I65KNALSX · pith_short_16: 3S6I65KNALSXAH7M · pith_short_8: 3S6I65KN

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/3S6I65KNALSXAH7M2VWYSDXPZW \
  | 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: dcbc8f754d02e5701fecd56d890eefcd812cc37efcfbc222fe589fa66a505713

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "91711d957e030687d34a172ae24c89fe360ccfdf0746f16120b3236796a2b685",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2015-02-09T23:51:24Z",
    "title_canon_sha256": "ae53447ef064af7434e97faf03d0b8c80929df548ffdff5121832754b52835a5"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1502.02739",
    "kind": "arxiv",
    "version": 1
  }
}