Pith Number

pith:ID6IZFLE

pith:2015:ID6IZFLE73RN3MMPE45XERWPFC

not attested not anchored not stored refs pending

Discrete averaging relations for micro to macro transition

Celia Reina, Chenchen Liu

arxiv:1509.06621 v1 · 2015-09-22 · cond-mat.mtrl-sci

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{ID6IZFLE73RN3MMPE45XERWPFC}

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	2026-05-18T01:11:51.335759Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

40fc8c9564fee2ddb18f273b7246cf28bda70dc05778c30bc35b06bbfba57329

Aliases

arxiv: 1509.06621 · arxiv_version: 1509.06621v1 · doi: 10.48550/arxiv.1509.06621 · pith_short_12: ID6IZFLE73RN · pith_short_16: ID6IZFLE73RN3MMP · pith_short_8: ID6IZFLE

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/ID6IZFLE73RN3MMPE45XERWPFC \
  | 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: 40fc8c9564fee2ddb18f273b7246cf28bda70dc05778c30bc35b06bbfba57329

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "44767a93676f94fabcd18b04b36c5ccc5f14d7429134df49e56cb413e7e5da21",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cond-mat.mtrl-sci",
    "submitted_at": "2015-09-22T14:36:48Z",
    "title_canon_sha256": "59afb22aa532c8b5267932833eecb78440f5c0e8e9517dcfe4356d48a497c1da"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1509.06621",
    "kind": "arxiv",
    "version": 1
  }
}