Pith Number

pith:4MEPQUEP

pith:2011:4MEPQUEPNBDQC5YJOOHKNVFY5U

not attested not anchored not stored refs pending

Effect of a crossing change on crossing number

Fengchun Lei, Longting Wu, Shan Liu, Shuting Shao

arxiv:1103.4695 v1 · 2011-03-24 · 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{4MEPQUEPNBDQC5YJOOHKNVFY5U}

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	2026-05-18T04:26:01.059249Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e308f8508f6847017709738ea6d4b8ed3373a726bbec703aaade03a5ae9cc13b

Aliases

arxiv: 1103.4695 · arxiv_version: 1103.4695v1 · doi: 10.48550/arxiv.1103.4695 · pith_short_12: 4MEPQUEPNBDQ · pith_short_16: 4MEPQUEPNBDQC5YJ · pith_short_8: 4MEPQUEP

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/4MEPQUEPNBDQC5YJOOHKNVFY5U \
  | 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: e308f8508f6847017709738ea6d4b8ed3373a726bbec703aaade03a5ae9cc13b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2ecddcffec337518400e27ef24072eacf18601ab6a0345478cdf3b2bdca9e9d7",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2011-03-24T08:18:22Z",
    "title_canon_sha256": "4810c72403bc93b309e84f79f6072396c215eb0b2f42e961bb96c4edcd1b3222"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1103.4695",
    "kind": "arxiv",
    "version": 1
  }
}