Pith Number

pith:KCJ2VHR2

pith:2020:KCJ2VHR2HYK3GRXMSHCQLDMJVE

not attested not anchored not stored refs pending

Cluster explorations of the loop soup on a metric graph related to the Gaussian free field

elie aidekon

arxiv:2009.05120 v1 · 2020-09-10 · math.PR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{KCJ2VHR2HYK3GRXMSHCQLDMJVE}

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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.

Cited by

1 paper in Pith

A switching identity for cable-graph loop soups and Gaussian free fields

Receipt and verification

First computed	2026-07-05T01:34:35.234211Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5093aa9e3a3e15b346ec91c5058d89a9233ba71a72c577c99ab3330856dd3e99

Aliases

arxiv: 2009.05120 · arxiv_version: 2009.05120v1 · doi: 10.48550/arxiv.2009.05120 · pith_short_12: KCJ2VHR2HYK3 · pith_short_16: KCJ2VHR2HYK3GRXM · pith_short_8: KCJ2VHR2

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/KCJ2VHR2HYK3GRXMSHCQLDMJVE \
  | 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: 5093aa9e3a3e15b346ec91c5058d89a9233ba71a72c577c99ab3330856dd3e99

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "03455a0c40a0658325985373b03006be043d1e0a174b274a25c82372011bfacc",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2020-09-10T19:39:04Z",
    "title_canon_sha256": "d6e3623711c399227ab6c1cc61098cfdf2d65a891e0e9eff57f661f26276fa9e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2009.05120",
    "kind": "arxiv",
    "version": 1
  }
}