Pith Number

pith:UDZGX7TB

pith:2021:UDZGX7TBD7CZQKENVJFNYR5IIW

not attested not anchored not stored refs pending

The category of simple graphs is coreflective in the comma category of groups under the free group functor

Christian Frank

arxiv:2103.03105 v5 · 2021-03-04 · math.CT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{UDZGX7TBD7CZQKENVJFNYR5IIW}

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	2026-07-05T06:12:21.912950Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a0f26bfe611fc598288daa4adc47a845a0e644869cf1a42a8e0994abfe74a4e1

Aliases

arxiv: 2103.03105 · arxiv_version: 2103.03105v5 · doi: 10.48550/arxiv.2103.03105 · pith_short_12: UDZGX7TBD7CZ · pith_short_16: UDZGX7TBD7CZQKEN · pith_short_8: UDZGX7TB

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/UDZGX7TBD7CZQKENVJFNYR5IIW \
  | 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: a0f26bfe611fc598288daa4adc47a845a0e644869cf1a42a8e0994abfe74a4e1

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "58ba7713d4b3d6d49c06c809e2926e4dbe66cd1b8b551f75a03a5afcad5b549c",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by-sa/4.0/",
    "primary_cat": "math.CT",
    "submitted_at": "2021-03-04T15:26:47Z",
    "title_canon_sha256": "c1895fa6a26f6d9808eea925733cedbd72b4636a26e3cf1dd1d62a71dedee563"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2103.03105",
    "kind": "arxiv",
    "version": 5
  }
}