persistentidentifiers.org

An identifier is a maintained relation between a string and an object. A string of numbers divorced from its identified object is no longer an identifier.

The persistence of the string is not the persistence of the identifier — it is what conceals the relation's death.

STRING MAINTAINED RELATION OBJECT an identifier STRING OBJECT SEVERED a numeral with the history of having identified

FIG. 1 — the cut is an obelus, the Alexandrian mark of custodial severance. In the registry it is written nowhere: no activity record, no tombstone, no delta but the count.

What is a persistent identifier? A string whose relation to its object is maintained indefinitely by a responsible organization — resolution, metadata, and citation continuity included.
What does persistence require? Custody of state: a record of what the string identified, since when, and what has changed. No public state-transition ledger exists for the world's largest research-data registry — 0 activity records logged any departure from findability.
What happens when the relation is severed? In the registrar's own deletion export: 1,309,351 removal events; in sampling, 203 of 204 deleted DOIs absent from the registry's public index, 0 of 25 retraction warnings surviving where the records persist elsewhere, and 0 restorations across all observed epochs.
Are DOIs persistent identifiers? Measure below.

The PID Erosion Observatory

Persistent Identifier Erosion Observatory — measuring whether persistent identifiers persist.

Instrument: EA-EROSION-01 · deposit #1045 · AXN:0421.EMPIRICAL.🎭📐🐝🎪🏷️🎇  ·  Operator: Lee Sharks

This document is the instrument specification and the public record of the PID Erosion Observatory. Every headline figure is reproducible from a public endpoint or a published capture-and-analysis script; each epoch preserves its requests, UTC observation times, scope, completion state, and error counts. The founding case involves deposits registered by the operator; all claims herein are independently replicable via the public API and the published epoch captures.
PROVENANCE · founded 2026-07-06 as the Platform Erosion Observatory (EA-EROSION-01, deposit #1045) · renamed the PID Erosion Observatory on 2026-07-12 upon acquisition of its sovereign domain, persistentidentifiers.org · the founding name remains in the deposit record · prior address platform-erosion-observatory.vercel.app remains live · this instrument logs its own state transitions.
130,559,831
findable DOIs in the DataCite registry — DC-E0 snapshot, 2026-07-11T03:58Z
replicatecurl "https://api.datacite.org/dois?page[size]=1" | jq .meta.total # returns the live total; compare to snapshot
4,418
DataCite client accounts represented in the public registry (client types include repositories, periodicals, IGSN catalogues, RAiD registries)
replicatecurl "https://api.datacite.org/clients?page[size]=1" | jq .meta.total
1,309,351
removal events in Zenodo's published deletion export — ZD-S1 snapshot 2026-06-07, preserved (upstream retains only three monthly snapshots)
replicatecurl -O https://zenodo.org/api/exporter/records-deleted.csv.gz
92.14%
of those rows have no citation_text — export-level citation retention: 7.86%. A proxy ceiling for tombstone continuity; landing-page tombstone compliance: audit pending
replicatecount rows with empty citation_text in the preserved ZD-S1 export; method deposited in EA-EROSION-01 §findings
0
public registry-wide historical series of per-client findability counts. Current per-client totals are queryable one at a time; their dated history — departures from findability, restorations — is preserved in no public longitudinal ledger. That history is this instrument's territory
replicatecurl "https://api.datacite.org/dois?client-id=cern.zenodo&page[size]=1" | jq .meta.total # current only; no history endpoint exists
100% / 92%
of sampled deleted records are absent from DataCite public findability / still present in OpenAlex — while the OpenAIRE Graph shows 0/54 across all deletion vintages, with no tombstone: the aggregators diverge completely, and absence is silent (XR-E1 + XR-E2, 2026-07-12)
replicatecurl https://www.alexanarch.org/data/zd-sample-crossregistry-epoch1-2026-07-12.json # seed, method, and per-DOI HTTP states
0/25
Zenodo-"retracted" records carrying a retraction flag where they persist in OpenAlex — the retraction warning propagates as silent absence in one graph and unflagged presence in another (ZD-A2, 2026-07-12)
replicatecurl https://www.alexanarch.org/data/zd-a2-category-audit-2026-07-12.json # per-record verdicts incl. oa_is_retracted
0
restorations documented across founding-case epochs FC-E1→FC-E3 (2026-06-22 → 2026-07-11, 19 days of observation; the triggering event precedes FC-E1 by 3 days)
replicatecurl -i "https://api.datacite.org/dois/10.5281/zenodo.14538882" # a founding-case DOI; expect 404 (absent from public findability)

The premise

DataCite's policy is that Findable and Registered DOIs cannot be deleted (DataCite Support: deletion policy) — but a Findable DOI can be moved to Registered state, which removes its metadata from public search, DataCite Commons, and the unauthenticated public API (DataCite Support: DOI states). The Handle may survive while public discoverability, metadata access, citation continuity, and provenance function are severed — and each of those functions must be measured separately.

No public registry-wide state-transition ledger has been identified by the Observatory. This was tested, not assumed: DataCite's per-DOI activities endpoint (/dois/{id}/activities) was probed for sampled founding-case DOIs and returned zero activity records — no creation history, and no severance event. (For at least one other publicly-absent DOI, historical create/update activities — including original metadata payloads — remain publicly served, while the departure from findability itself appears in no activity record.) The transition is unlogged. A DOI that stops being counted stops silently.

Therefore the only public severance signal is the delta. The Observatory takes dated snapshots of findability state — registry-wide per-client counts, and per-DOI state for watched sets — and records what changed between epochs. A present-state check tells you what exists now. Only custody of the state history can tell you what existed, when it changed, what was lost, and whether it was restored.

Epoch ledger

Epochs are namespaced by lane: DC (DataCite registry census) · FC (founding-case DOI probes) · ZD (Zenodo deletion-export snapshots) · XR (cross-registry propagation sampling) · ZD-A (deletion-export analyses). From DC-E1 forward, each capture preserves: observed-at UTC · endpoint · exact request · scope · expected/completed/error counts · response hashes · harness commit.

EpochDateFindingCapture
DC-E02026-07-11Registry-wide census in progress — 2,405 / 4,418 clients completed (2,013 failed or pending retry; weekly automated sweep continues). Completed clients cover 62,665,297 findable DOIs. Registry total findable at snapshot: 130,559,831 (03:58Z).JSON
FC-E12026-06-22Full probe of the founding-case capture set: 871/871 keys absent from public findability (HTTP 404 at the public API). Pattern type-correlated: concept layer absent, version layer retained. Pre-severance metadata backup published same day.#867 · #868
FC-E22026-07-03871/871 still absent. Zero state changes observed.JSON
FC-E32026-07-11871/871 still absent (03:50:27Z, 12-way parallel probe, per-DOI HTTP states preserved). Zero restorations documented across FC-E1→FC-E3, an interval spanning active governance correspondence. Includes epoch zero of the per-client count series (cern.zenodo: 11,928,577 findable).JSON
ZD-S12026-06-07Monthly deleted-records export preserved: 1,309,351 rows, 2017–2026. 88.27% flagged spam; 764,082 events in 2024 alone. 92.14% carry no citation_text (export-level retention 7.86%). Each unpreserved month is permanent substrate loss.#1045
ZD-S22026-07-12Deletion export re-captured: 1,322,007 rows+12,656 removal events since ZD-S1 (35 days). Citation-text absence 91.30% (retention 8.70%). Label-structure analysis: the 87.5% “spam” share is a process label, not an adjudication record — 68.0% of spam-labeled rows carry the account-stratum note “User was blocked”; 89.6% sit in same-day, same-note batches of ≥1,000; ≤0.1% show a process signature compatible with per-record review; and the spam pathway writes no citation_text at all, making the export's citation absence largely a pathway artifact. Export gzip sha256 preserved in the XR-E1 capture.JSON
XR-E12026-07-12Cross-registry propagation sample (new XR lane): seeded stratified sample (n=150; seed 20260712; strata spam/out-of-scope/take-down-request/retracted; founding-case day excluded) probed against DataCite and OpenAlex. 150/150 absent from DataCite public findability — severance is universal across all removal classes. 138/150 (92%) persist in OpenAlex: out-of-scope 40/40 (100%), spam 57/60 (95%), take-down-request 23/25 (92%), retracted 18/25 (72%). The founding-case cohort (out-of-scope, 97.2% shadow persistence) behaves as a typical member of its removal class. OpenAIRE Graph lane pending; re-runnable from the same seed.JSON
XR-E22026-07-12OpenAIRE Graph vintage/lag test (n=54; six deletion vintages 2017–2026; 57/60 rate-budgeted calls; same seed, round-robin). 0/54 sampled deleted records present in the OpenAIRE Graph API — across every vintage and removal class, with no tombstone or withdrawal marker: absence is silent. The aggregators diverge completely: OpenAlex retains 42/54 (a step at its ~2020 ingest horizon, flat ~85–90% after — structural within its window). Founding-case controls split at a one-day boundary: the 2026-preFC bin (deletions through June 18) is fully absent, while the Space Ark concept record (deleted June 19) is served in full — fourteen authors, operator ORCID, instances pointing at the tombstoned zenodo.org URL. The boundary is observed; its mechanism is not — a release-cycle ingest horizon and case-specific retention during active governance correspondence are both consistent with the data and cannot be distinguished from outside. OpenAIRE's own changelog (v10.2.0, released 2025-04-04) documents the population-level mechanism: a blacklist of 1.2Mi DOIs from Zenodo-withdrawn records, systematically removed from the Graph together with their relations — the changelog itself records a ~5% (254K) drop in project-linked research products from the operation, and v10.6.0 expanded blacklist construction to parent DOIs. What remains indistinguishable from outside is per-record history: whether any individual absent DOI was removed by that process or never ingested — no public state-transition ledger exists, which is this instrument's founding argument. Outlier: zenodo.1196638 (spam, deleted 2018-07-03) still findable at DataCite eight years later — combined XR severance propagation 203/204 (99.5%).JSON · payload
ZD-A12026-07-12Spam-label content audit (n=300; 150 per pathway; seeded; published mechanical rubric v2, with the v1→v2 rubric correction documented as part of the record). The label is substantially corroborated at content level: 46.7% pattern-confirmed spam, with inspection showing the uncorroborated residual dominated by pattern-evading SEO and ebook-piracy queries. The measured collateral: 1.0% [95% CI 0.34–2.90] of spam-labeled records carry affirmative scholarship indicia — extrapolated, on the order of 104 records [~4K–34K] across the class, including cited research deleted by account block. Staff-adjudicated removals show higher confirmation (58.0% vs 35.3%) and zero scholarship-signal collateral (0/150 vs 3/150): adjudication works where it occurs; the account-block pathway, source of 68% of the class, is where the collateral lives. The asymmetry is the finding: this audit measured an error rate from outside, using surviving metadata shadows — the removal process itself wrote no per-record evidence in either direction, so its errors are invisible to the operator and uncorrectable by design.JSON
ZD-A22026-07-12Cross-category audit: the collateral gradient. Same rubric and indicators as ZD-A1, applied across the remaining removal taxonomy (n=390; seven categories). Scholarship-signal collateral rises tenfold down the classifier-confidence gradient: spam 1.0% → out-of-scope 10.0% [5.8–16.7] → empty-reason 24.0% [14.3–37.4] (take-down 58.0%, as expected for copyright actions against real content). Note structure: exactly two categories are account-stratum — spam (68.0% "User was blocked") and out-of-scope (99.2%); all others are record-level. Out-of-scope is the habitat of nonstandard scholarship — sampled collateral includes ORCID-bearing research documents, multilingual reference series, and AI-native serial work — extrapolating to ~6,700 records [3,900–11,200] in that category alone; ~22,500 across the taxonomy. Category corroborations are reported where found (test-record: 0% collateral). Retraction propagation: 0/25 — of Zenodo-"retracted" records still present in OpenAlex, none carries is_retracted=true: the removal class whose purpose is public warning propagates as silent absence in one graph and unflagged live scholarship in another.JSON
ZD-A32026-07-12Temporal audit: regime periodization and label migration. The removal taxonomy has four eras (exact, population-level): pre-taxonomy 2017–2019 (86% of 2017 removals carry no reason); spam wars 2020–2024 (spam = 95–99.7% of every year, culminating in the 2024 account-block purge, 761,778 rows); curation interlude 2025 (record-level categories diversify); scope enforcement 2026 — the out-of-scope category has 0 rows before 2024 and 68,215 in the first half of 2026 (53.9% of the year's removals). Label migration: the account-block bulk pathway is born in 2024 labeled spam and fires in 2026 labeled out-of-scope — the mechanism is constant, the label migrated, and the destination label carries 10× the measured collateral (ZD-A2 vs ZD-A1). Sampled within-spam drift: scholarship-signal 0.0% across 2020–2024 (three bins, n=105) rising to 14.3% (2025) and 8.6% (2026) with ORCID emergence — late-era catches include serially-numbered theory work, activist self-archiving, and a Japanese essay series; no commercial signature. Two readings are held open — enforcement-band narrowing vs LLM-era spam mimicry — with a pre-registered prediction (2026-07-12, in the capture): if the band is narrowing, the diversity of the retained corpus will show contraction in step; the hosted-corpus study is designed and deferred.JSON

Severance taxonomy

A DOI can remain technically extant while its documentary functions are severed. The functions fail separately and must be classified separately:

Public-findability severance
A previously Findable DOI ceases to appear in DataCite Commons and the unauthenticated public API. Where the Handle continues to resolve, the condition is consistent with a Findable → Registered transition unless contrary evidence appears; a public-API 404 establishes absence from public findability, and the state interpretation is recorded as inference, not observation.
Metadata severance
Observable loss or mutation of substantial fields in metadata that remains accessible.
Resolution severance
The DOI stops resolving, or enters redirect failure.
Object severance
The landing resolves but the deposited object is gone.
Tombstone transition
The object is replaced by a removal notice preserving the citation — or by nothing. Landing-page tombstone compliance is audited separately from export-level citation retention.
Provenance severance
Creator, affiliation, related identifiers, versions, or citations removed or altered.
Target substitution
The DOI resolves, but to materially different content.
Custodial transfer
Provider, repository, or responsible organization changes.
Partial restoration
Resolution returns; the prior object, metadata, or provenance does not.

Exhibit A: the founding case — application of the taxonomy

Zenodo account termination → public-findability severance, June 2026

862 scholarly deposits · 1,817 DOIs registered through DataCite · one enforcement action

2026-06-19Event. Zenodo account terminated; records removed at the repository layer (HTTP 410 Gone at zenodo.org). ≤ 2026-06-22Public-findability severance observed no later than FC-E1: 871 capture keys absent from the public API — type-correlated, the concept (citation-layer) DOIs absent while version DOIs were largely retained (97.9% of retained records carry IsVersionOf links). Provenance severance: creator-name search collapsed across the operator's ORCID and 15 distinct heteronymous scholarly names (sweep method in #868). 2026-06-22FC-E1 audit + shadow persistence. Pre-severance metadata backup published (#867); empirical paper "DOIs ≠ Persistent Identifiers" (#868). OpenAlex retained 844 of the 868 well-formed severed DOIs (97.2%) with 2,275,008 characters of abstract text — the graph kept the records; the registry's public index dropped them. 2026-07-03FC-E2. 871/871 keys still absent. Zero changes. 2026-07-10Reception persistence. Google AI Mode served severed zenodo.org/records/ URLs as live scholarly citations, three weeks after tombstoning — documented as capture marx-johannes-sigil-heteronym-adoption-20260710 in the Capture Registry, with the served URLs and surface screenshots preserved. Removal did not reach machine reception; it removed only the provenance apparatus that made attribution verifiable. 2026-07-11FC-E3. 871/871 keys still absent (03:50:27Z); per-DOI HTTP states in the public capture. Sampled per-DOI activity trails: zero public records; no severance event logged.
RESTORATION STATUS: NONE DOCUMENTED · FC-E1 → FC-E3 · 2026-06-22 to 2026-07-11 · governance correspondence pending (CERN ODP)

Units reconciliation

862
deposit records removed at the repository layer on 2026-06-19.
1,817
DOIs registered through DataCite across those deposits (concept + version layers).
871
keys in the founding-case capture set: DOIs absent from public findability at FC-E1. Disclosed data-quality note: 3 of the 871 keys are malformed truncations (zenodo.1, .18, .189) — artifacts of the original sweep's key handling. They return 404 trivially, as any nonexistent DOI would.
868
well-formed severed DOIs (871 keys − 3 artifacts). This is the denominator of the OpenAlex shadow-persistence audit.
851
severed DOIs whose metadata survives in no other findable DataCite record — unique documentary loss at the public index. (Registered-state metadata cannot be inspected through the public API; the claim is scoped to findability.)
946
DOIs from the original 1,817 that remain findable; 97.9% carry IsVersionOf — the retained layer is the version layer, the absent layer is the citation-target concept layer.

This incident is Exhibit A because every element is publicly reconstructible: the pre-event state, the event, the epochs, the shadow copies, the reception layer, and the non-restoration. Most severance events in the registry have none of this — which is the point of the instrument.

Operator position — policy proposal

Operator commentary · distinct from the empirical record above

Severance is not the only available response to classifier or policy flags. A controlled metadata value — classifier-flagged, with genre refinements — asserts a fact about the registrar's process rather than a verdict about the work: it can be applied without requiring the registrar to adjudicate the scholarly truth, merit, or final status of the work. Reclassification preserves the citation graph, creates the first public baseline of what content classifiers remove from the scholarly record, and gives training-ingestion pipelines exactly what they claim to want: labeled material to filter at their own discretion. You cannot filter what you have deleted the labels for. A formal proposal is in preparation.

The class that cannot be severed silently

Operator commentary · distinct from the empirical record above

Content-derived identifiers

A string divorced from its object is no longer an identifier. An identifier derived from its object cannot be divorced from it undetected: either half verifies the other.

Assigned identifiers — DOIs among them — depend on an institution maintaining the relation between string and object; the epochs above measure what happens when the institution stops. Content-derived identifiers compute the string from the object, so the relation is a mathematical property rather than an institutional promise. The class is established practice, not proposal: SWHIDs (Software Heritage's ISO-standardized intrinsic identifiers), IPFS CIDs, and git commit hashes all identify by content. Severance of a content-derived identifier is detectable by anyone holding either half — which is to say, the alternative to institutional memory is not better institutions but identifiers that do not need them.

The AXN is this archive's implementation: a content-derived hex identifier paired with a six-emoji glyph serving as a human-verifiable checksum, chained under SHA-256 integrity. This instrument is itself identified by one:

AXN:0421.EMPIRICAL.🎭📐🐝🎪🏷️🎇  →  EA-EROSION-01, deposit #1045 (the PID Erosion Observatory's own charter)
verification: recompute from content · registry: alexanarch.org data spine · no institution required to hold the relation open

Had the 1,817 DOIs of the founding case been paired with content-derived identifiers, their severance would have been detectable, provable, and reversible from any surviving copy. The records above show what the assigned-identifier regime does instead.

Replication

# live registry findable total (compare to the DC-E0 snapshot above)
curl "https://api.datacite.org/dois?page[size]=1" | jq .meta.total
# any client's current findable count (current only — no public history exists)
curl "https://api.datacite.org/dois?client-id=cern.zenodo&page[size]=1" | jq .meta.total
# a founding-case DOI (expect 404: absent from public findability)
curl -i "https://api.datacite.org/dois/10.5281/zenodo.14538882"
# its public activity trail (expect zero records: the transition is unlogged)
curl "https://api.datacite.org/dois/10.5281/zenodo.14538882/activities"
# the epoch captures (raw, per-DOI, with observation timestamps)
curl https://www.alexanarch.org/data/datacite-epoch3-2026-07-11.json
curl https://www.alexanarch.org/data/datacite-registrywide-epoch0-2026-07-11.json
# zenodo's own deletion export (preserve it — upstream keeps only 3 snapshots)
curl -O https://zenodo.org/api/exporter/records-deleted.csv.gz

Essays

Foundations