Pith Number

pith:6CL75W2B

pith:2019:6CL75W2BYCRPUA5ECNHC6S2EA7

not attested not anchored not stored refs pending

Volume of line bundles via valuation vectors (different from Okounkov bodies)

Oliver Braunling

arxiv:1903.04317 v1 · 2019-03-11 · math.AG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{6CL75W2BYCRPUA5ECNHC6S2EA7}

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	2026-05-17T23:51:35.793512Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f097fedb41c0a2fa03a4134e2f4b4407db63bb3a7c21ac91645ff1c658a74e7e

Aliases

arxiv: 1903.04317 · arxiv_version: 1903.04317v1 · doi: 10.48550/arxiv.1903.04317 · pith_short_12: 6CL75W2BYCRP · pith_short_16: 6CL75W2BYCRPUA5E · pith_short_8: 6CL75W2B

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/6CL75W2BYCRPUA5ECNHC6S2EA7 \
  | 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: f097fedb41c0a2fa03a4134e2f4b4407db63bb3a7c21ac91645ff1c658a74e7e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7d3c46b78995c730b8acb186a753d600411ba5f7970123445ebc1e7062f6aac9",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2019-03-11T14:17:13Z",
    "title_canon_sha256": "0a42bb7c0d8a1f592aea9b93083a0b8e3196ce326f114adc1c98d23547fc7957"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1903.04317",
    "kind": "arxiv",
    "version": 1
  }
}