Pith Number

pith:NPTTEOFY

pith:2026:NPTTEOFYQZYRWPVMVE2NHTU6RF

not attested not anchored not stored refs pending

On polyharmonic Kirchhoff double phase problems without AR-conditions

Ashutosh Dixit, Tuhina Mukherjee

arxiv:2606.24827 v1 · 2026-06-23 · 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{NPTTEOFYQZYRWPVMVE2NHTU6RF}

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	2026-06-24T01:15:43.381743Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6be73238b886711b3eaca934d3ce9e894c9ee8a25f32a5ecde287719b40c4e1c

Aliases

arxiv: 2606.24827 · arxiv_version: 2606.24827v1 · doi: 10.48550/arxiv.2606.24827 · pith_short_12: NPTTEOFYQZYR · pith_short_16: NPTTEOFYQZYRWPVM · pith_short_8: NPTTEOFY

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/NPTTEOFYQZYRWPVMVE2NHTU6RF \
  | 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: 6be73238b886711b3eaca934d3ce9e894c9ee8a25f32a5ecde287719b40c4e1c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d5db4daeb4e9164704a0989fafcaef319dcb14f154e92fcd3ae669acaa7a9d70",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2026-06-23T17:11:21Z",
    "title_canon_sha256": "8e7c49dd2361ab42981293ac91c732d75c922660acbe8c06e979ea54eb4e7a02"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.24827",
    "kind": "arxiv",
    "version": 1
  }
}