Pith Number

pith:ODSAJMKW

pith:2019:ODSAJMKWWBHVTZXAVJCC7TJQRK

not attested not anchored not stored refs pending

Minimal Codes From Characteristic Functions Not Satisfying The Ashikhmin-Barg Condition

Julien Sorci

arxiv:1912.12769 v1 · 2019-12-30 · math.CO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{ODSAJMKWWBHVTZXAVJCC7TJQRK}

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	2026-07-05T00:29:03.256424Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

70e404b156b04f59e6e0aa442fcd308abed987ed4d462f8b6c4ab6bcceb56a7f

Aliases

arxiv: 1912.12769 · arxiv_version: 1912.12769v1 · doi: 10.48550/arxiv.1912.12769 · pith_short_12: ODSAJMKWWBHV · pith_short_16: ODSAJMKWWBHVTZXA · pith_short_8: ODSAJMKW

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/ODSAJMKWWBHVTZXAVJCC7TJQRK \
  | 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: 70e404b156b04f59e6e0aa442fcd308abed987ed4d462f8b6c4ab6bcceb56a7f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d1c2cfed1eeb308f5c2217dc14501986bc838579f932aaa413206f44276898c7",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2019-12-30T01:01:53Z",
    "title_canon_sha256": "d2246803519862626e411dfc72276f2ff556f02f3bd10943de37612a7aeda3c4"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1912.12769",
    "kind": "arxiv",
    "version": 1
  }
}