Pith Number

pith:C26YPNIP

pith:2026:C26YPNIPBSKYYJYTO25YHFKJ5Z

not attested not anchored not stored refs pending

Refined blow-up criteria and global solutions for triangular cross-diffusion systems

Alexandre Bertolino (LJLL, DMA)

arxiv:2607.01857 v1 · 2026-07-02 · math.AP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{C26YPNIPBSKYYJYTO25YHFKJ5Z}

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	2026-07-03T01:17:31.786614Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

16bd87b50f0c958c271376bb839549ee6868f018422870fba800d82af8c0441d

Aliases

arxiv: 2607.01857 · arxiv_version: 2607.01857v1 · doi: 10.48550/arxiv.2607.01857 · pith_short_12: C26YPNIPBSKY · pith_short_16: C26YPNIPBSKYYJYT · pith_short_8: C26YPNIP

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/C26YPNIPBSKYYJYTO25YHFKJ5Z \
  | 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: 16bd87b50f0c958c271376bb839549ee6868f018422870fba800d82af8c0441d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "68083873f529b1783894a2582506837d4cdea758fa42ab92f241497bb91df084",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2026-07-02T08:16:56Z",
    "title_canon_sha256": "535e37c652a4fd0eb0dbe84f727f01f09a294f79afa189ff4e3cafef7ac0badc"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.01857",
    "kind": "arxiv",
    "version": 1
  }
}