Pith Number

pith:474UKWIO

pith:2017:474UKWIOAG2BA3ESWBQPRTOKFT

not attested not anchored not stored refs pending

Entropy and quasimorphisms

Michael Brandenbursky, Micha{\l} Marcinkowski

arxiv:1707.06020 v3 · 2017-07-19 · math.GT · math.DS · math.GR · math.SG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{474UKWIOAG2BA3ESWBQPRTOKFT}

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	2026-05-17T23:52:08.446207Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e7f945590e01b4106c92b060f8cdca2cea3c8dcd0247d56ca5a42dd64c48c2f9

Aliases

arxiv: 1707.06020 · arxiv_version: 1707.06020v3 · doi: 10.48550/arxiv.1707.06020 · pith_short_12: 474UKWIOAG2B · pith_short_16: 474UKWIOAG2BA3ES · pith_short_8: 474UKWIO

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/474UKWIOAG2BA3ESWBQPRTOKFT \
  | 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: e7f945590e01b4106c92b060f8cdca2cea3c8dcd0247d56ca5a42dd64c48c2f9

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d5b4924e7a87e32d36e9aa6188c3601e49bd328786af980310721f2f534ca3a5",
    "cross_cats_sorted": [
      "math.DS",
      "math.GR",
      "math.SG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2017-07-19T11:09:53Z",
    "title_canon_sha256": "438e85e6c9a90ce0e55a5b4433d56df1ffc26db6a81471aba91533c1daa65feb"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1707.06020",
    "kind": "arxiv",
    "version": 3
  }
}