Pith Number

pith:HPTRAJPI

pith:2015:HPTRAJPIW2SBEM4FTZOXSE3IAO

not attested not anchored not stored refs pending

Ramanujan Coverings of Graphs

Chris Hall, Doron Puder, William F. Sawin

arxiv:1506.02335 v3 · 2015-06-08 · math.CO · math.GR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{HPTRAJPIW2SBEM4FTZOXSE3IAO}

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	2026-05-18T00:29:02.068020Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3be71025e8b6a41233859e5d79136803aa1256af0cd6926326413510c46165dd

Aliases

arxiv: 1506.02335 · arxiv_version: 1506.02335v3 · doi: 10.48550/arxiv.1506.02335 · pith_short_12: HPTRAJPIW2SB · pith_short_16: HPTRAJPIW2SBEM4F · pith_short_8: HPTRAJPI

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/HPTRAJPIW2SBEM4FTZOXSE3IAO \
  | 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: 3be71025e8b6a41233859e5d79136803aa1256af0cd6926326413510c46165dd

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "682d2713b17360647b1fc966412d42723c679343bf60127ae7d416a1d1af931e",
    "cross_cats_sorted": [
      "math.GR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2015-06-08T01:54:10Z",
    "title_canon_sha256": "617904729105ee3a998e67019038ac303e8234e2d3e58dff3b7285cc8bab30fe"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1506.02335",
    "kind": "arxiv",
    "version": 3
  }
}