Pith Number

pith:D5WCWNDV

pith:2013:D5WCWNDVWQRH5JB7YVFYLPNHQG

not attested not anchored not stored refs pending

Projections in the curve complex arising from covering maps

Robert Tang

arxiv:1310.6987 v1 · 2013-10-25 · math.GT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{D5WCWNDVWQRH5JB7YVFYLPNHQG}

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	2026-05-18T00:21:01.001797Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1f6c2b3475b4227ea43fc54b85bda78199fe4355883ac805336386f9dc750665

Aliases

arxiv: 1310.6987 · arxiv_version: 1310.6987v1 · doi: 10.48550/arxiv.1310.6987 · pith_short_12: D5WCWNDVWQRH · pith_short_16: D5WCWNDVWQRH5JB7 · pith_short_8: D5WCWNDV

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/D5WCWNDVWQRH5JB7YVFYLPNHQG \
  | 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: 1f6c2b3475b4227ea43fc54b85bda78199fe4355883ac805336386f9dc750665

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ca76a57125e20b2c1e45680acd837b49499e123e728f1abe0b64a2d4f043c49a",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2013-10-25T17:31:27Z",
    "title_canon_sha256": "87f306efc7b2dc06f79cd3fd91e4ff540c23ed9b617a959dfd8ff9f7cf4f77cf"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1310.6987",
    "kind": "arxiv",
    "version": 1
  }
}