{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2021:EALO5A4FPGW6BNLSRIOFDA2UBK","short_pith_number":"pith:EALO5A4F","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"},"canonical_sha256":"2016ee838579ade0b5728a1c5183540a86869932b1aab8f882eb2f58541141b8","source":{"kind":"arxiv","id":"2110.13893","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2110.13893","created_at":"2026-07-05T06:43:43Z"},{"alias_kind":"arxiv_version","alias_value":"2110.13893v3","created_at":"2026-07-05T06:43:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2110.13893","created_at":"2026-07-05T06:43:43Z"},{"alias_kind":"pith_short_12","alias_value":"EALO5A4FPGW6","created_at":"2026-07-05T06:43:43Z"},{"alias_kind":"pith_short_16","alias_value":"EALO5A4FPGW6BNLS","created_at":"2026-07-05T06:43:43Z"},{"alias_kind":"pith_short_8","alias_value":"EALO5A4F","created_at":"2026-07-05T06:43:43Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2021:EALO5A4FPGW6BNLSRIOFDA2UBK","target":"record","payload":{"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"},"canonical_sha256":"2016ee838579ade0b5728a1c5183540a86869932b1aab8f882eb2f58541141b8","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"},"source_kind":"arxiv","source_id":"2110.13893","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T06:43:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dULB8sHT9+smUmQR5o7V/jv3qXMI7qjbHKY7OO9up62px950OoulzxX1dJIHdiTaFDnvICGTup79rjpm6nszCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-06T13:53:14.454485Z"},"content_sha256":"2b4a5fac47144c42e059dabc2afa8cd2dc5a61ec8e8979423ae5e2a4f1569dff","schema_version":"1.0","event_id":"sha256:2b4a5fac47144c42e059dabc2afa8cd2dc5a61ec8e8979423ae5e2a4f1569dff"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2021:EALO5A4FPGW6BNLSRIOFDA2UBK","target":"graph","payload":{"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T06:43:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lfeVdiydzteLy1I9jTDFZ8N5/KLsSz9pm9qYqiVfOksfkoiOktQvRNcXfI8t2zX74+ctvgixn26Ja3g2rJSgCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-06T13:53:14.454860Z"},"content_sha256":"a648675bc8732d1678f998f2e783732aab965468cbe02739efc87974632dba4c","schema_version":"1.0","event_id":"sha256:a648675bc8732d1678f998f2e783732aab965468cbe02739efc87974632dba4c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/EALO5A4FPGW6BNLSRIOFDA2UBK/bundle.json","state_url":"https://pith.science/pith/EALO5A4FPGW6BNLSRIOFDA2UBK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/EALO5A4FPGW6BNLSRIOFDA2UBK/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-07-06T13:53:14Z","links":{"resolver":"https://pith.science/pith/EALO5A4FPGW6BNLSRIOFDA2UBK","bundle":"https://pith.science/pith/EALO5A4FPGW6BNLSRIOFDA2UBK/bundle.json","state":"https://pith.science/pith/EALO5A4FPGW6BNLSRIOFDA2UBK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/EALO5A4FPGW6BNLSRIOFDA2UBK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:EALO5A4FPGW6BNLSRIOFDA2UBK","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"45fe5dbcbfde41c8d4f5e09d450abf7eff7e7317aae6d8ea3b9b24e68332a734","cross_cats_sorted":["cond-mat.stat-mech","math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2021-10-26T17:48:49Z","title_canon_sha256":"5ce308bb7864b7dbdae58c248f2c0126152b756585285184a5abaa6e2ecf9e6e"},"schema_version":"1.0","source":{"id":"2110.13893","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2110.13893","created_at":"2026-07-05T06:43:43Z"},{"alias_kind":"arxiv_version","alias_value":"2110.13893v3","created_at":"2026-07-05T06:43:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2110.13893","created_at":"2026-07-05T06:43:43Z"},{"alias_kind":"pith_short_12","alias_value":"EALO5A4FPGW6","created_at":"2026-07-05T06:43:43Z"},{"alias_kind":"pith_short_16","alias_value":"EALO5A4FPGW6BNLS","created_at":"2026-07-05T06:43:43Z"},{"alias_kind":"pith_short_8","alias_value":"EALO5A4F","created_at":"2026-07-05T06:43:43Z"}],"graph_snapshots":[{"event_id":"sha256:a648675bc8732d1678f998f2e783732aab965468cbe02739efc87974632dba4c","target":"graph","created_at":"2026-07-05T06:43:43Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2110.13893/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"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","authors_text":"Jacob Calvert","cross_cats":["cond-mat.stat-mech","math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2021-10-26T17:48:49Z","title":"Existence of a Phase Transition in Harmonic Activation and Transport"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2110.13893","kind":"arxiv","version":3},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:2b4a5fac47144c42e059dabc2afa8cd2dc5a61ec8e8979423ae5e2a4f1569dff","target":"record","created_at":"2026-07-05T06:43:43Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"45fe5dbcbfde41c8d4f5e09d450abf7eff7e7317aae6d8ea3b9b24e68332a734","cross_cats_sorted":["cond-mat.stat-mech","math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2021-10-26T17:48:49Z","title_canon_sha256":"5ce308bb7864b7dbdae58c248f2c0126152b756585285184a5abaa6e2ecf9e6e"},"schema_version":"1.0","source":{"id":"2110.13893","kind":"arxiv","version":3}},"canonical_sha256":"2016ee838579ade0b5728a1c5183540a86869932b1aab8f882eb2f58541141b8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2016ee838579ade0b5728a1c5183540a86869932b1aab8f882eb2f58541141b8","first_computed_at":"2026-07-05T06:43:43.436220Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T06:43:43.436220Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"AZcal0nSww1cJLMsC748V8xbz1f2mx/gbJN2LcuvV7eIpSdJGsRnq7gpxyBfWSMiSwYL9bVaESQRwyX1QIDNCA==","signature_status":"signed_v1","signed_at":"2026-07-05T06:43:43.436713Z","signed_message":"canonical_sha256_bytes"},"source_id":"2110.13893","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2b4a5fac47144c42e059dabc2afa8cd2dc5a61ec8e8979423ae5e2a4f1569dff","sha256:a648675bc8732d1678f998f2e783732aab965468cbe02739efc87974632dba4c"],"state_sha256":"66b6114e8a9c4979661fdaf615a256792be810f6e8ed1469befb23619c06950c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gVeclA3wVW3bjxetqR6v1BtrV+Ux92bAJ+tnmtes1ZQOWbaf7JtzZqw50SC4gBe4c0FJ37o2ev+l6XS6e6LYCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-06T13:53:14.456844Z","bundle_sha256":"1f8277d7cb349e28c22887c7f8bc5668332014bdab989d0e63071687f1440a01"}}