{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:C4RP4S6ZKZE4NOAVWTWKR2OELG","short_pith_number":"pith:C4RP4S6Z","canonical_record":{"source":{"id":"1707.08875","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-07-27T14:22:44Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"ea6738082e3f24830c2dce5b9f27cb0c23ec86d5c476d4ca586623ffa572a33a","abstract_canon_sha256":"3a5b44520119cfec9d4d7134c5ec2e395a32a7415404343e605d03443a1a4289"},"schema_version":"1.0"},"canonical_sha256":"1722fe4bd95649c6b815b4eca8e9c45980b0dd2668c1aa195fd7bb60b3498c96","source":{"kind":"arxiv","id":"1707.08875","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1707.08875","created_at":"2026-05-18T00:09:31Z"},{"alias_kind":"arxiv_version","alias_value":"1707.08875v1","created_at":"2026-05-18T00:09:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1707.08875","created_at":"2026-05-18T00:09:31Z"},{"alias_kind":"pith_short_12","alias_value":"C4RP4S6ZKZE4","created_at":"2026-05-18T12:31:08Z"},{"alias_kind":"pith_short_16","alias_value":"C4RP4S6ZKZE4NOAV","created_at":"2026-05-18T12:31:08Z"},{"alias_kind":"pith_short_8","alias_value":"C4RP4S6Z","created_at":"2026-05-18T12:31:08Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:C4RP4S6ZKZE4NOAVWTWKR2OELG","target":"record","payload":{"canonical_record":{"source":{"id":"1707.08875","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-07-27T14:22:44Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"ea6738082e3f24830c2dce5b9f27cb0c23ec86d5c476d4ca586623ffa572a33a","abstract_canon_sha256":"3a5b44520119cfec9d4d7134c5ec2e395a32a7415404343e605d03443a1a4289"},"schema_version":"1.0"},"canonical_sha256":"1722fe4bd95649c6b815b4eca8e9c45980b0dd2668c1aa195fd7bb60b3498c96","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:09:31.001530Z","signature_b64":"719K3WtQYvnPvuOtrwFPQfVvveWvtlpiO1kOXiDNC4UZ3j/fEZCH9xa5qvK7TvsK6Ycv0gmRgH/axPnXa9LCCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1722fe4bd95649c6b815b4eca8e9c45980b0dd2668c1aa195fd7bb60b3498c96","last_reissued_at":"2026-05-18T00:09:31.000850Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:09:31.000850Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1707.08875","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:09:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VbTE1MI5mkx4f2UsPea1yXbyNMtlcVHNiH4kWM83zrHG9MmcNj0WMtMPjo5sO9J7vDZCZQ1ugRTjmayUHspBBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T13:40:19.111445Z"},"content_sha256":"9a1052bbb2675cd5c9a8a0cb2b519523dabd9d0d77d588f311b388e2daaf680b","schema_version":"1.0","event_id":"sha256:9a1052bbb2675cd5c9a8a0cb2b519523dabd9d0d77d588f311b388e2daaf680b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:C4RP4S6ZKZE4NOAVWTWKR2OELG","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Zero-temperature dynamics in the dilute Curie-Weiss model","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.PR","authors_text":"Charles M. Newman, Daniel L. Stein, Reza Gheissari","submitted_at":"2017-07-27T14:22:44Z","abstract_excerpt":"We consider the Ising model on a dense Erd\\H{o}s--R\\'enyi random graph, $\\mathcal G(N,p)$, with $p>0$ fixed---equivalently, a disordered Curie--Weiss Ising model with $\\mbox{Ber}(p)$ couplings---at zero temperature. The disorder may induce local energy minima in addition to the two uniform ground states. In this paper we prove that, starting from a typical initial configuration, the zero-temperature dynamics avoids all such local minima and absorbs into a predetermined one of the two uniform ground states. We relate this to the local MINCUT problem on dense random graphs; namely with high prob"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.08875","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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":"2026-05-18T00:09:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"O5z79SuWE6QB87COImVQXTy9s5J+BA70SFOvs7AZC6zf2vY+0GBIFln6ALVlEJnJq7EGdnRoINtHLj7Wrxc2Dw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T13:40:19.111813Z"},"content_sha256":"1ca19a4536f6e4d9552582b4a2a9a029e6e06c5d11412cc547c5b897318767d7","schema_version":"1.0","event_id":"sha256:1ca19a4536f6e4d9552582b4a2a9a029e6e06c5d11412cc547c5b897318767d7"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/C4RP4S6ZKZE4NOAVWTWKR2OELG/bundle.json","state_url":"https://pith.science/pith/C4RP4S6ZKZE4NOAVWTWKR2OELG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/C4RP4S6ZKZE4NOAVWTWKR2OELG/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":"2026-05-30T13:40:19Z","links":{"resolver":"https://pith.science/pith/C4RP4S6ZKZE4NOAVWTWKR2OELG","bundle":"https://pith.science/pith/C4RP4S6ZKZE4NOAVWTWKR2OELG/bundle.json","state":"https://pith.science/pith/C4RP4S6ZKZE4NOAVWTWKR2OELG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/C4RP4S6ZKZE4NOAVWTWKR2OELG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:C4RP4S6ZKZE4NOAVWTWKR2OELG","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":"3a5b44520119cfec9d4d7134c5ec2e395a32a7415404343e605d03443a1a4289","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-07-27T14:22:44Z","title_canon_sha256":"ea6738082e3f24830c2dce5b9f27cb0c23ec86d5c476d4ca586623ffa572a33a"},"schema_version":"1.0","source":{"id":"1707.08875","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1707.08875","created_at":"2026-05-18T00:09:31Z"},{"alias_kind":"arxiv_version","alias_value":"1707.08875v1","created_at":"2026-05-18T00:09:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1707.08875","created_at":"2026-05-18T00:09:31Z"},{"alias_kind":"pith_short_12","alias_value":"C4RP4S6ZKZE4","created_at":"2026-05-18T12:31:08Z"},{"alias_kind":"pith_short_16","alias_value":"C4RP4S6ZKZE4NOAV","created_at":"2026-05-18T12:31:08Z"},{"alias_kind":"pith_short_8","alias_value":"C4RP4S6Z","created_at":"2026-05-18T12:31:08Z"}],"graph_snapshots":[{"event_id":"sha256:1ca19a4536f6e4d9552582b4a2a9a029e6e06c5d11412cc547c5b897318767d7","target":"graph","created_at":"2026-05-18T00:09:31Z","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"},"paper":{"abstract_excerpt":"We consider the Ising model on a dense Erd\\H{o}s--R\\'enyi random graph, $\\mathcal G(N,p)$, with $p>0$ fixed---equivalently, a disordered Curie--Weiss Ising model with $\\mbox{Ber}(p)$ couplings---at zero temperature. The disorder may induce local energy minima in addition to the two uniform ground states. In this paper we prove that, starting from a typical initial configuration, the zero-temperature dynamics avoids all such local minima and absorbs into a predetermined one of the two uniform ground states. We relate this to the local MINCUT problem on dense random graphs; namely with high prob","authors_text":"Charles M. Newman, Daniel L. Stein, Reza Gheissari","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-07-27T14:22:44Z","title":"Zero-temperature dynamics in the dilute Curie-Weiss model"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.08875","kind":"arxiv","version":1},"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":"sha256:9a1052bbb2675cd5c9a8a0cb2b519523dabd9d0d77d588f311b388e2daaf680b","target":"record","created_at":"2026-05-18T00:09:31Z","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":"3a5b44520119cfec9d4d7134c5ec2e395a32a7415404343e605d03443a1a4289","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-07-27T14:22:44Z","title_canon_sha256":"ea6738082e3f24830c2dce5b9f27cb0c23ec86d5c476d4ca586623ffa572a33a"},"schema_version":"1.0","source":{"id":"1707.08875","kind":"arxiv","version":1}},"canonical_sha256":"1722fe4bd95649c6b815b4eca8e9c45980b0dd2668c1aa195fd7bb60b3498c96","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1722fe4bd95649c6b815b4eca8e9c45980b0dd2668c1aa195fd7bb60b3498c96","first_computed_at":"2026-05-18T00:09:31.000850Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:09:31.000850Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"719K3WtQYvnPvuOtrwFPQfVvveWvtlpiO1kOXiDNC4UZ3j/fEZCH9xa5qvK7TvsK6Ycv0gmRgH/axPnXa9LCCA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:09:31.001530Z","signed_message":"canonical_sha256_bytes"},"source_id":"1707.08875","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9a1052bbb2675cd5c9a8a0cb2b519523dabd9d0d77d588f311b388e2daaf680b","sha256:1ca19a4536f6e4d9552582b4a2a9a029e6e06c5d11412cc547c5b897318767d7"],"state_sha256":"43f615aa86751717c710b1a0e1199991046892e534eb9f1aa3303b18a15d90f9"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"W4u0V/cPvx/Zwq3/ynvSfq1Tdygk20uIVCPn+uzmaTgdFB4ANLlfUSqBnQUtS9RGjkLb30OrkaFWCPOzcUOtAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T13:40:19.113891Z","bundle_sha256":"a8bef3c6b7a3c84b9a3a50dd5d10706d181cf50dd2860f3f90e1371c724b505e"}}