Pith Number

pith:QZETMK4R

pith:2010:QZETMK4R5IONKQ5AGDLSIDLMTJ

not attested not anchored not stored refs pending

Density estimates for phase transitions with a trace

Enrico Valdinoci, Yannick Sire

arxiv:1011.6617 v1 · 2010-11-30 · 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{QZETMK4R5IONKQ5AGDLSIDLMTJ}

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	2026-05-18T04:34:26.493907Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

8649362b91ea1cd543a030d7240d6c9a52f5fb3361e4c83fb639aa2dfe7a79a2

Aliases

arxiv: 1011.6617 · arxiv_version: 1011.6617v1 · doi: 10.48550/arxiv.1011.6617 · pith_short_12: QZETMK4R5ION · pith_short_16: QZETMK4R5IONKQ5A · pith_short_8: QZETMK4R

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/QZETMK4R5IONKQ5AGDLSIDLMTJ \
  | 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: 8649362b91ea1cd543a030d7240d6c9a52f5fb3361e4c83fb639aa2dfe7a79a2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3c0a86b82f7a4e39af7c57ed3b8327c652a0569cad7997b4888aca87a4b96359",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2010-11-30T17:40:01Z",
    "title_canon_sha256": "26f38ae794699bd405606a256ec96e60a27dc50bd470981126e2983761afc65c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1011.6617",
    "kind": "arxiv",
    "version": 1
  }
}