{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2021:EALO5A4FPGW6BNLSRIOFDA2UBK","short_pith_number":"pith:EALO5A4F","schema_version":"1.0","canonical_sha256":"2016ee838579ade0b5728a1c5183540a86869932b1aab8f882eb2f58541141b8","source":{"kind":"arxiv","id":"2110.13893","version":3},"attestation_state":"computed","paper":{"title":"Existence of a Phase Transition in Harmonic Activation and Transport","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech","math-ph","math.MP"],"primary_cat":"math.PR","authors_text":"Jacob Calvert","submitted_at":"2021-10-26T17:48:49Z","abstract_excerpt":"Harmonic activation and transport (HAT) is a stochastic process that rearranges finite subsets of $\\mathbb{Z}^d$, one element at a time. Given a finite set $U \\subset \\mathbb{Z}^d$ with at least two elements, HAT removes $x$ from $U$ according to the harmonic measure of $x$ in $U$, and then adds $y$ according to the probability that simple random walk from $x$, conditioned to hit the remaining set, steps from $y$ when it first does so. In particular, HAT conserves the number of elements in $U$.\n  We study the classification of HAT as recurrent or transient, as the dimension $d$ and number of e"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2110.13893","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2021-10-26T17:48:49Z","cross_cats_sorted":["cond-mat.stat-mech","math-ph","math.MP"],"title_canon_sha256":"5ce308bb7864b7dbdae58c248f2c0126152b756585285184a5abaa6e2ecf9e6e","abstract_canon_sha256":"45fe5dbcbfde41c8d4f5e09d450abf7eff7e7317aae6d8ea3b9b24e68332a734"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T06:43:43.436713Z","signature_b64":"AZcal0nSww1cJLMsC748V8xbz1f2mx/gbJN2LcuvV7eIpSdJGsRnq7gpxyBfWSMiSwYL9bVaESQRwyX1QIDNCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2016ee838579ade0b5728a1c5183540a86869932b1aab8f882eb2f58541141b8","last_reissued_at":"2026-07-05T06:43:43.436220Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T06:43:43.436220Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Existence of a Phase Transition in Harmonic Activation and Transport","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech","math-ph","math.MP"],"primary_cat":"math.PR","authors_text":"Jacob Calvert","submitted_at":"2021-10-26T17:48:49Z","abstract_excerpt":"Harmonic activation and transport (HAT) is a stochastic process that rearranges finite subsets of $\\mathbb{Z}^d$, one element at a time. Given a finite set $U \\subset \\mathbb{Z}^d$ with at least two elements, HAT removes $x$ from $U$ according to the harmonic measure of $x$ in $U$, and then adds $y$ according to the probability that simple random walk from $x$, conditioned to hit the remaining set, steps from $y$ when it first does so. In particular, HAT conserves the number of elements in $U$.\n  We study the classification of HAT as recurrent or transient, as the dimension $d$ and number of e"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2110.13893","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2110.13893/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"2110.13893","created_at":"2026-07-05T06:43:43.436275+00:00"},{"alias_kind":"arxiv_version","alias_value":"2110.13893v3","created_at":"2026-07-05T06:43:43.436275+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2110.13893","created_at":"2026-07-05T06:43:43.436275+00:00"},{"alias_kind":"pith_short_12","alias_value":"EALO5A4FPGW6","created_at":"2026-07-05T06:43:43.436275+00:00"},{"alias_kind":"pith_short_16","alias_value":"EALO5A4FPGW6BNLS","created_at":"2026-07-05T06:43:43.436275+00:00"},{"alias_kind":"pith_short_8","alias_value":"EALO5A4F","created_at":"2026-07-05T06:43:43.436275+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/EALO5A4FPGW6BNLSRIOFDA2UBK","json":"https://pith.science/pith/EALO5A4FPGW6BNLSRIOFDA2UBK.json","graph_json":"https://pith.science/api/pith-number/EALO5A4FPGW6BNLSRIOFDA2UBK/graph.json","events_json":"https://pith.science/api/pith-number/EALO5A4FPGW6BNLSRIOFDA2UBK/events.json","paper":"https://pith.science/paper/EALO5A4F"},"agent_actions":{"view_html":"https://pith.science/pith/EALO5A4FPGW6BNLSRIOFDA2UBK","download_json":"https://pith.science/pith/EALO5A4FPGW6BNLSRIOFDA2UBK.json","view_paper":"https://pith.science/paper/EALO5A4F","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2110.13893&json=true","fetch_graph":"https://pith.science/api/pith-number/EALO5A4FPGW6BNLSRIOFDA2UBK/graph.json","fetch_events":"https://pith.science/api/pith-number/EALO5A4FPGW6BNLSRIOFDA2UBK/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/EALO5A4FPGW6BNLSRIOFDA2UBK/action/timestamp_anchor","attest_storage":"https://pith.science/pith/EALO5A4FPGW6BNLSRIOFDA2UBK/action/storage_attestation","attest_author":"https://pith.science/pith/EALO5A4FPGW6BNLSRIOFDA2UBK/action/author_attestation","sign_citation":"https://pith.science/pith/EALO5A4FPGW6BNLSRIOFDA2UBK/action/citation_signature","submit_replication":"https://pith.science/pith/EALO5A4FPGW6BNLSRIOFDA2UBK/action/replication_record"}},"created_at":"2026-07-05T06:43:43.436275+00:00","updated_at":"2026-07-05T06:43:43.436275+00:00"}