Pith Number

pith:4L3QFWXG

pith:2023:4L3QFWXG6O2O3W7JZA726QHKRS

not attested not anchored not stored refs pending

Multiarc and curve graphs are hierarchically hyperbolic

Michael C. Kopreski

arxiv:2311.04356 v3 · 2023-11-07 · 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{4L3QFWXG6O2O3W7JZA726QHKRS}

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

On fixed points of pseudo-Anosov maps

Receipt and verification

First computed	2026-07-05T08:22:34.610172Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e2f702dae6f3b4eddbe9c83faf40ea8ca2d7371695fe751664b52d66c03581b5

Aliases

arxiv: 2311.04356 · arxiv_version: 2311.04356v3 · doi: 10.48550/arxiv.2311.04356 · pith_short_12: 4L3QFWXG6O2O · pith_short_16: 4L3QFWXG6O2O3W7J · pith_short_8: 4L3QFWXG

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/4L3QFWXG6O2O3W7JZA726QHKRS \
  | 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: e2f702dae6f3b4eddbe9c83faf40ea8ca2d7371695fe751664b52d66c03581b5

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b6a5e3c9fb4c690924823025c23ae7b611cc89e7ae17bb73e6e06b67c1cf3705",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2023-11-07T21:37:39Z",
    "title_canon_sha256": "e22431f8f21a36bab54e3ce25fb5fe55482284f703f41096637e36e53d0c4f14"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2311.04356",
    "kind": "arxiv",
    "version": 3
  }
}