Pith Number

pith:DNZS4GDI

pith:2017:DNZS4GDIURTELCQAFBH2O3X76B

not attested not anchored not stored refs pending

Phase transitions in graphs on orientable surfaces

Michael Mo{\ss}hammer, Mihyun Kang, Philipp Spr\"ussel

arxiv:1708.07671 v1 · 2017-08-25 · 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{DNZS4GDIURTELCQAFBH2O3X76B}

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	2026-05-18T00:36:42.403659Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1b732e1868a466458a00284fa76efff05c01dec6ab10f0dc983da74e2d427f9d

Aliases

arxiv: 1708.07671 · arxiv_version: 1708.07671v1 · doi: 10.48550/arxiv.1708.07671 · pith_short_12: DNZS4GDIURTE · pith_short_16: DNZS4GDIURTELCQA · pith_short_8: DNZS4GDI

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/DNZS4GDIURTELCQAFBH2O3X76B \
  | 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: 1b732e1868a466458a00284fa76efff05c01dec6ab10f0dc983da74e2d427f9d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "586afc9627af8792512b3de699025ad875963542ee58dece01a4729caedfd983",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2017-08-25T09:54:00Z",
    "title_canon_sha256": "fe48aec68fd2d82509c2a3c50b99998751575e22b9eadee23dfcbf9d5abc05d4"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1708.07671",
    "kind": "arxiv",
    "version": 1
  }
}