Pith Number

pith:UO7GIX4O

pith:2018:UO7GIX4OGUYYTQ36VQGV3H6A3V

not attested not anchored not stored refs pending

Algorithmic aspects of immersibility and embeddability

Fedor Manin, Shmuel Weinberger

arxiv:1812.09413 v4 · 2018-12-21 · math.GT · cs.CG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{UO7GIX4OGUYYTQ36VQGV3H6A3V}

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	2026-07-05T09:22:35.242297Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a3be645f8e353189c37eac0d5d9fc0dd594fdb68df99d41c96f1da6e3be67c57

Aliases

arxiv: 1812.09413 · arxiv_version: 1812.09413v4 · doi: 10.48550/arxiv.1812.09413 · pith_short_12: UO7GIX4OGUYY · pith_short_16: UO7GIX4OGUYYTQ36 · pith_short_8: UO7GIX4O

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/UO7GIX4OGUYYTQ36VQGV3H6A3V \
  | 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: a3be645f8e353189c37eac0d5d9fc0dd594fdb68df99d41c96f1da6e3be67c57

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c26ec6dff551e4db5b5e736bbca83667d34f2ef72432aa72d244ab344076a441",
    "cross_cats_sorted": [
      "cs.CG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2018-12-21T23:34:29Z",
    "title_canon_sha256": "40684b8eff15854dd705e9357c39cda5670e60cfae7b581e6d4438a1164a35f1"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1812.09413",
    "kind": "arxiv",
    "version": 4
  }
}