Pith Number

pith:7B2UPKIA

pith:2026:7B2UPKIAMD224ERZU52UB4UCBS

not attested not anchored not stored refs pending

Alternating Extremes in Graceful Labelings of Full Binary Trees and Spider Trees

Bogdan Dumitru, Mihai Nacu

arxiv:2607.12597 v1 · 2026-07-14 · 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{7B2UPKIAMD224ERZU52UB4UCBS}

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	2026-07-15T01:22:05.915339Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f87547a90060f5ae1239a77540f2820c9a1839d056c8e0f90569661299cf0736

Aliases

arxiv: 2607.12597 · arxiv_version: 2607.12597v1 · doi: 10.48550/arxiv.2607.12597 · pith_short_12: 7B2UPKIAMD22 · pith_short_16: 7B2UPKIAMD224ERZ · pith_short_8: 7B2UPKIA

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/7B2UPKIAMD224ERZU52UB4UCBS \
  | 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: f87547a90060f5ae1239a77540f2820c9a1839d056c8e0f90569661299cf0736

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "eea9415bca81f56c2294d34c1ebe1407355b60aa14e62e06ebc25be54103631d",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2026-07-14T10:14:29Z",
    "title_canon_sha256": "6280f1d55a93fa8a1de3a91b746ea813539ab12f0f121d8deb299c58c7b507c2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.12597",
    "kind": "arxiv",
    "version": 1
  }
}