Pith Number

pith:PHV2WJJB

pith:2019:PHV2WJJBCMQSVSWUDOOUUT4ED6

not attested not anchored not stored refs pending

Patterns in sets of positive density in trees and affine buildings

A. Fish, J. Parkinson, M. Bj\"orklund

arxiv:1907.05825 v1 · 2019-07-12 · math.CO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{PHV2WJJBCMQSVSWUDOOUUT4ED6}

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	2026-05-17T23:40:44.286213Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

79ebab252113212acad41b9d4a4f841f89c917e7f113a83bd2890092208234bb

Aliases

arxiv: 1907.05825 · arxiv_version: 1907.05825v1 · doi: 10.48550/arxiv.1907.05825 · pith_short_12: PHV2WJJBCMQS · pith_short_16: PHV2WJJBCMQSVSWU · pith_short_8: PHV2WJJB

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/PHV2WJJBCMQSVSWUDOOUUT4ED6 \
  | 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: 79ebab252113212acad41b9d4a4f841f89c917e7f113a83bd2890092208234bb

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4ca5d815ad3e1ff0787a350ed4b00f8f2deb8c7c5d58966744c5ee19b9ef95f3",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2019-07-12T16:24:41Z",
    "title_canon_sha256": "6e6b80e76863b0bd4f7f48b2e5dfac3e3fdd59517de81e49dbb0212df7572422"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1907.05825",
    "kind": "arxiv",
    "version": 1
  }
}