Pith Number

pith:CS4RYQ53

pith:2026:CS4RYQ53Y3ZHNK3EGK3AREICJV

not attested not anchored not stored refs pending

On the K\"ahler MMP and the transcendental base-point-free theorem

Christopher Hacon, Lingyao Xie

arxiv:2607.24986 v1 · 2026-07-27 · 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{CS4RYQ53Y3ZHNK3EGK3AREICJV}

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	2026-07-29T00:24:56.497225Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

14b91c43bbc6f276ab6432b60891024d5e5e7e1332d70b5acc80756529bbe122

Aliases

arxiv: 2607.24986 · arxiv_version: 2607.24986v1 · doi: 10.48550/arxiv.2607.24986 · pith_short_12: CS4RYQ53Y3ZH · pith_short_16: CS4RYQ53Y3ZHNK3E · pith_short_8: CS4RYQ53

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/CS4RYQ53Y3ZHNK3EGK3AREICJV \
  | 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: 14b91c43bbc6f276ab6432b60891024d5e5e7e1332d70b5acc80756529bbe122

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "61d04438f6aa62926e8ac319b73a29aa68c7a4110758b62e4fbe7535dc6ac97e",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2026-07-27T18:39:33Z",
    "title_canon_sha256": "2ae2472b75280f703a6b0aec7868961091680ab7a217025b113f29db2671cbd2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.24986",
    "kind": "arxiv",
    "version": 1
  }
}