Pith Number

pith:KHEQHE6U

pith:2015:KHEQHE6UYMOCLXCVA6A5FTSW3H

not attested not anchored not stored refs pending

Casson invariants via virtual counting

Junwu Tu

arxiv:1512.02322 v1 · 2015-12-08 · math.DG · 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{KHEQHE6UYMOCLXCVA6A5FTSW3H}

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	2026-05-18T01:24:45.014554Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

51c90393d4c31c25dc550781d2ce56d9edf026b91d51d3ac015dae0d18bdfbd9

Aliases

arxiv: 1512.02322 · arxiv_version: 1512.02322v1 · doi: 10.48550/arxiv.1512.02322 · pith_short_12: KHEQHE6UYMOC · pith_short_16: KHEQHE6UYMOCLXCV · pith_short_8: KHEQHE6U

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/KHEQHE6UYMOCLXCVA6A5FTSW3H \
  | 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: 51c90393d4c31c25dc550781d2ce56d9edf026b91d51d3ac015dae0d18bdfbd9

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3afdd5ba3ee6aee2fa4773193d5c2f74139b390e2b6d661843401416e9a47efd",
    "cross_cats_sorted": [
      "math.SG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2015-12-08T04:28:52Z",
    "title_canon_sha256": "c7f75ebb2e4b20a8e428836dffaaad07ee595e3d0b8a1a715e09275314a875cc"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1512.02322",
    "kind": "arxiv",
    "version": 1
  }
}