Pith Number

pith:UUYF3MV7

pith:2025:UUYF3MV74NIGEYKFX3CJQMA7BN

not attested not anchored not stored refs pending

Branched $\alpha$-combinatorial Ricci flows on closed surfaces with Euler characteristic $\chi\le 0$

Aijin Lin, Guohao Chen, Rongyuan Liu, Wenjun Li

arxiv:2505.24762 v4 · 2025-05-30 · math.DG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{UUYF3MV74NIGEYKFX3CJQMA7BN}

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	2026-07-05T11:32:29.910845Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a5305db2bfe350626145bec498301f0b5c4fa1392fd475d995cd292de1b0cda8

Aliases

arxiv: 2505.24762 · arxiv_version: 2505.24762v4 · doi: 10.48550/arxiv.2505.24762 · pith_short_12: UUYF3MV74NIG · pith_short_16: UUYF3MV74NIGEYKF · pith_short_8: UUYF3MV7

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/UUYF3MV74NIGEYKFX3CJQMA7BN \
  | 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: a5305db2bfe350626145bec498301f0b5c4fa1392fd475d995cd292de1b0cda8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b9b6bbb5438b544d8e60b29e4214ad973604921d39ebdbcfc4bd1b2260dec38e",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2025-05-30T16:20:49Z",
    "title_canon_sha256": "21f9e03d9b47df0faf47aa4938374fbf329f607b028f9c36a56f069d46dae101"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2505.24762",
    "kind": "arxiv",
    "version": 4
  }
}